Download Two Essays on Managerial Behaviors in the Mutual Fund Industry

Georgia State University
ScholarWorks @ Georgia State University
Finance Dissertations
Department of Finance
6-13-2008
Two Essays on Managerial Behaviors in the Mutual
Fund Industry Essay 1: A Life-Cycle Analysis of
Performance and Growth in U.S. Mutual Funds
Essay 2: Can Mutual Fund Window-Dressing
Promote Fund Flows?
Leng Ling
Follow this and additional works at: http://scholarworks.gsu.edu/finance_diss
Recommended Citation
Ling, Leng, "Two Essays on Managerial Behaviors in the Mutual Fund Industry Essay 1: A Life-Cycle Analysis of Performance and
Growth in U.S. Mutual Funds Essay 2: Can Mutual Fund Window-Dressing Promote Fund Flows?." Dissertation, Georgia State
University, 2008.
http://scholarworks.gsu.edu/finance_diss/13
This Dissertation is brought to you for free and open access by the Department of Finance at ScholarWorks @ Georgia State University. It has been
accepted for inclusion in Finance Dissertations by an authorized administrator of ScholarWorks @ Georgia State University. For more information,
please contact [email protected].
Permission to Borrow
In presenting this dissertation as a partial fulfillment of the requirements for an advanced
degree from Georgia State University, I agree that the Library of the University shall
make it available for inspection and circulation in accordance with its regulations
governing materials of this type. I agree that permission to quote from, or to publish this
dissertation may be granted by the author or, in his/her absence, the professor under
whose direction it was written or, in his absence, by the Dean of the Robinson College of
Business. Such quoting, copying, or publishing must be solely for scholarly purposes and
does not involve potential financial gain. It is understood that any copying from or
publication of this dissertation which involves potential gain will not be allowed without
written permission of the author.
__________Leng Ling______________
signature of author
1
Notice to Borrowers
All dissertations deposited in the Georgia State University Library must be used only in
accordance with the stipulations prescribed by the author in the preceding statement.
The author of this dissertation is:
Leng Ling
1322 Briarwood Road B-11
Atlanta, GA 30319
The director of this dissertation is:
Gerald D. Gay and Jason T. Greene
Department of Finance
J. Mack Robinson College of Business
Georgia State University
Atlanta, GA 30303-3083
Users of this dissertation not regularly enrolled as students at Georgia State University
are required to attest acceptance of the preceding stipulations by signing below. Libraries
borrowing this dissertation for the use of their patrons are required to see that each user
records here the information requested.
Name of User
Address
Date
2
TWO ESSAYS ON MANAGERIAL BEHAVIORS
IN THE MUTUAL FUND INDUSTRY
BY
LENG LING
A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree
of
Doctor of Philosophy
in the Robinson College of Business
of
Georgia State University
GEORGIA STATE UNIVERSITY
ROBINSON COLLEGE OF BUSINESS
2008
3
Copyright by
Leng Ling
2008
4
ACCEPTANCE
This dissertation was prepared under the direction of the candidate’s Dissertation
Committee. It has been approved and accepted by all members of that committee, and it
has been accepted in partial fulfillment of the requirements for the degree of Doctor in
Philosophy in Business Administration in the Robinson College of Business of Georgia
State University.
________________________
Dean
Robinson College of Business
Dissertation Committee:
_________Gerald D. Gay______
_________Jason T. Greene_____
_________Harley E. Ryan______
_________Conrad S. Ciccotello_
5
ABSTRACT
TWO ESSAYS ON MANAGERIAL BEHAVIORS
IN THE MUTUAL FUND INDUSTRY
By
LENG LING
June 4, 2008
Committee Chair:
Dr. Gerald D. Gay and Jason T. Greene
Major Department:
Finance
ESSAY 1: DOES MUTUAL FUND WINDOW-DRESSING PROMOTE
FUND FLOWS?
I investigate the effectiveness of window-dressing as a potential strategy to be
used by mutual fund managers to promote fund flows. Using a rank gap measure as a
proxy for the likelihood that window-dressing has occurred, I find that fund investors as
whole punish those managers who are suspected to have engaged in window-dressing.
That is, I find a negative relation between the window-dressing measure and net fund
flows in subsequent quarters after controlling for fund performance, size, expense ratio,
and other pertinent characteristics. I also find that window-dressing leads to higher
trading activities and lower fund performance.
ESSAY 2: A LIFE CYCLE ANALYSIS OF PERFORMANCE AND GROWTH
IN U.S. MUTUAL FUNDS
I propose a five-stage growth model to describe the life cycle evolution of mutual
funds and show that mutual funds exhibit distinctive performance, size, expense ratios,
asset turnover, and other pertinent characteristics through stages of incubation, high-
6
growth, low-growth, maturity, and decline. I also investigate the viability of managerial
strategies to affect a fund’s life cycle evolution and find that changing a declining fund’s
investment objective is effective in rejuvenating asset growth and thus repositioning the
fund to younger life cycle stages. However, the strategy of adding portfolio managers
appears to have no such rejuvenation effect.
7
Does Mutual Fund Window-Dressing Promote Fund Flows?
Leng Ling*
Georgia State University
This version: June 3, 2008
Abstract
We investigate the effectiveness of window-dressing as a potential strategy to be used by
mutual fund managers to promote fund flows. Using a rank gap measure as a proxy for the
likelihood that window-dressing has occurred, we find that fund investors as whole punish those
managers who are suspected to have engaged in window-dressing. That is, we find a negative
relation between the window-dressing measure and net fund flows in subsequent quarters after
controlling for fund performance, size, expense ratio, and other pertinent characteristics. We also
find that window-dressing leads to higher trading activities and lower fund performance.
JEL Classification: G11; G20
Keywords: Mutual funds; Window dressing; Managerial behavior; Fund flows
* I thank my dissertation committee members, Gerald D. Gay (co-chair), Jason T. Greene (co-chair),
Conrad S. Ciccotello, and Harley E. Ryan for their valuable advice. I am grateful to Mark Chen, Marcin
Kacperczyk, Jayant Kale, Omesh Kini, Reza S. Mahani, and Laura Starks for their helpful comments and
constructive suggestions. Any errors that remain are mine. Contact information: Department of Finance, J.
Mack Robinson College of Business, Georgia State University, Atlanta, GA 30303-3083. Tel: 1-404-4137314; fax: 1-404-413-7312. E-mail address: [email protected].
8
1. Introduction
Mutual funds are required to report their portfolio holdings following the end of each
quarter.1 A number of articles in both financial press and academic literature suggest that prior to
the reporting date some equity fund managers may engage in window-dressing, whereby they
purchase or increase their holdings in stocks that have good performance recently (winners) and
unload poorly performing stocks (losers) to look better to current and potential investors.2 The
underlying premise is that investors base their investment decisions on observed portfolio
holdings, in addition to other information such as fund performance. Managers who windowdress expect fund investors to respond positively to a portfolio that shows more winners by
adding investment and to withdraw money from a fund that holds more losers.
The extant mutual fund literature has found evidence consistent with window-dressing
behavior of fund managers (see, Lakonishok, Shleifer, Thaler, and Vishny, 1991; Sias and Starks,
1997; He, Ng, and Wang, 2004; Ng and Wang, 2004; Meier and Schaumburg, 2004). These
studies, however, do not investigate the effect of window-dressing on fund flows. We extend this
literature by investigating the effectiveness of window-dressing as a strategy to promote fund
1
Under the Securities Exchange Act of 1934 and the Investment Company Act of 1940, mutual fund
managers were required to transmit a report to their shareholders semiannually. In 1975, Congress enacted
section 13 (f) of the Securities Exchange Act to increase the public availability of information on securities
holdings by institutional investors. Under this section, an institutional investment manager that exercises
investment discretion over portfolios with an aggregate value of $100 million or more must file quarterly
reports of portfolio holdings on Form 13F within 60 days after the end of each quarter. Although funds
were required to report semiannually after an amendment in 1985, a majority of managers voluntarily
disclose their portfolio holdings on a quarterly basis. Effective May 10, 2004, the U.S. Securities and
Exchange Commission requires investment companies file their complete portfolio schedule as of the end
of the first and the third fiscal quarters on Form N-Q, in addition to the annual and semiannual reports filed
on Form N-CSR and N-CSRS, respectively. Furthermore, schedules must be filed within 60 days after the
end of each quarter.
Source: (1) The Investment Company Act of 1940, Section 30. (2) The Securities Exchange Act of 1934,
Section 13 (f). (3) Cici, Gibson, and Moussawi (2006). (4) http://www.sec.gov/rules/final/33-8393.htm#IB.
(5) http://www.sec.gov/divisions/investment/guidance/13fpt2.htm.
2
There could be other types of window dressing. (1) Managers may decrease their holdings in high-risky
securities prior to the reporting date in order to make their portfolios appear less risky (Musto, 1997, 1999;
Morey and O’Neal, 2006). (2) At the last trading date of the quarter, managers may purchase stocks already
held to drive up stock prices and thereafter quarter-end fund values, a practice known as “portfolio
pumping”, “leaning for the tape”, or “marking up” (Carhart, Kaniel, Musto, and Reed, 2002). (3) Managers
may invest in securities that deviate from their stated fund objectives and eliminate those assets prior to the
reporting date (Meier and Schaumburg, 2004).
9
flows, using a sample of 27,286 quarterly reports filed by actively managed U.S. equity funds for
the period of March 1980 through December 2005.
This study also contributes to the literature by developing a new approach to detect
unobserved window-dressing behavior of fund managers. Since window-dressing occurrence
cannot be ascertained with certainty, we construct a rank gap measure as a proxy for the
likelihood that window-dressing has occurred. The rationale for this approach is that, on average,
a poorly performing fund has a high percentage of its assets invested in losers but low percentage
in winners. In contrast, a well performing fund has the opposite. Thus, observing a poorly
performing fund with a high percentage of assets in winners and a low percentage of assets in
losers suggests a greater window-dressing likelihood. Based on this reasoning, for each quarter
and each fund sector we rank funds in descending order by quarterly return and find the percentile
rank of return, with funds in the first percentile being the best performing funds. Similarly, we
find their percentile rank of winner proportion in descending order, where winner proportion is
the percentage of a fund’s assets invested in the winning stocks for the quarter. Also, we find
their percentile rank of loser proportion in ascending order, where loser proportion is the
percentage of a fund’s assets invested in the losing stocks for the quarter.
In the absence of window-dressing, a poorly performing fund should have a low percentile
rank of fund performance, a low percentile rank of winner proportion, and a low percentile rank
of loser proportion. If a fund has a low percentile rank of performance but relatively high
percentile ranks of winner and loser proportions, the resulting rank inconsistency suggests that the
fund manager has engaged in window-dressing. The larger the rank inconsistency, the higher
likelihood that window-dressing has occurred. We define the rank gap measure as the difference
between the rank of fund performance and the average of the ranks of winner and loser
proportions. The results of several tests strongly suggest that this measure is a reasonable proxy
for the unobserved window-dressing behavior. For instance, we find that rank gap is positively
related to trade volume in both contemporary and subsequent quarters, a relation that is consistent
10
with the conventional understanding that window-dressing involves unnecessary trading activities
of buying winners and selling losers.
The empirical results show that, on average, the window-dressing strategy does not promote
fund flows. We find that net fund flows in the subsequent quarter are negatively related to the
rank gap measure after controlling for fund performance and other pertinent characteristics
including size, age, loads, expense ratio, asset turnover, and investment objective. It appears that
fund investors indeed examine disclosed portfolio holdings. Furthermore, they infer managers’
window-dressing behavior and punish suspected managers by reducing their investment in the
funds. Further analysis shows that this negative response is from fund flows beginning in the third
month of the next quarter. There is no statistically significant relation between window-dressing
and fund flows in the first two months of the subsequent quarter. The U.S. Securities and
Exchange Commission (SEC) requires mutual fund managers file their quarterly reports of
portfolio holdings within 60 days after the end of a quarter. This rule actually allows managers to
file their reports with delay. Using both SEC’s Edgar database and Thomson Financial mutual
fund holding database, we find that a large number of mutual funds delayed their reports for
around 60 days. That means that investors typically do not observe portfolio holdings until two
months after the end of the quarter. We also find that the effect of window-dressing on fund flows
can last for two quarters.
Consistent with He, Ng, and Wang (2004) and Meier and Schaumburg (2004), we find that a
manager is more likely to engage in window-dressing if his fund obtains lower past performance
than his peers. Since window-dressing could be detected and punished with reduced fund flows,
why do some managers especially those of poorly performing funds nevertheless do it and take
the risk it involves? We propose that these managers adopt the window-dressing strategy to affect
investors’ perception of managers’ stock selection skill, and they are able to hide their windowdressing strategy under some circumstances.
11
Because the SEC allows managers to file their reports with 60-day delay, a large number of
mutual funds postpone their portfolio disclosure. Poorly performing managers could benefit from
window-dressing with delayed reports. If a poorly performing manager window-dresses and fund
performance improves for whatever reason in the subsequent quarter, it is not easy for investors
to tell if this manager has engaged in window-dressing or he has stock selection skill as long as
the disclosed winners do not depreciate much. Fund investors are likely to believe that this
manager has stock selection skill because it is natural for investors to attribute improved fund
performance to the disclosed high proportion of assets invested in winning stocks. On the other
hand, if this unskilled manager experiences poor performance again in the following quarter, his
window-dressing behavior will be detected. However, he has little to lose because he already
faced a threat of being replaced at the end of the year because of the poor performance observed
in the preceding quarter. In contrast, managers of well performing funds have lower incentives to
window-dress because these managers benefit from good fund performance that attracts more
investment and they do not want to be punished with reduced fund flows.
Kacperczyk, Sialm, and Zheng (2006) create a return gap measure, the difference between a
fund’s reported return and the return of a hypothetical portfolio that invests in the fund’s
disclosed end-of-period holdings. They propose that this measure captures the effect of multiple
managerial actions including the pursuit of window-dressing behavior. For robustness, we repeat
all analyses using return gap as a proxy for window-dressing. We find that fund flows in the first
month of the quarter are sensitive to return gap of the prior quarter-ending month while fund
flows in the second and third subsequent months are not. This finding is inconsistent with the fact
that managers typically disclose their portfolio holdings with an approximate one to two months
lag. We also perform tests that show that our rank gap measure contains more information to
explain fund flows than return gap does.
The rest of the paper proceeds as follows. Section 2 reviews the literature. Section 3
describes the data and main variables used. Section 4 develops a rank gap measure to detect the
12
unobserved window-dressing behavior of mutual fund managers. Section 5 investigates the effect
of window-dressing on fund flows in subsequent periods. Section 6 reports the results of tests for
robustness. Section 7 concludes this study.
2. Literature review
Lakonishok, Shleifer, Thaler, and Vishny (1991) examine the quarterly holdings of 769
equity pension funds from 1985 to 1989. They estimate purchase and sales based on portfolio
changes over quarter-end and compare trading in the first three quarters with that in the fourth
quarter. Their results show that funds sell more losers in the fourth quarter. Since their method
compares the purchase and sales over quarter-end, it would not be able to test whether a fund
manager has engaged in window-dressing during a particular quarter.
Sias and Starks (1997) examine the trading activity of individual and institutional investors
at year-end and find that institutions sell fewer winners in the fourth calendar quarter than the first
quarter of the subsequent year, which is consistent with the window-dressing hypothesis.
Following Lakonishok et al. (1991), He, Ng, and Wang (2004) examine the quarterly
holdings of different types of institutions and show that banks, life insurance companies, mutual
funds, and investment companies who invest on behalf of their clients sell more poorly
performing stocks during the last quarter than the first three quarters of the year. Moreover, this
trading behavior is more pronounced for institutions whose portfolios have underperformed the
market. Ng and Wang (2004) investigate the relation between institutional trading and turn-ofthe-year effect in stock returns. Their results indicate that institutions sell more extreme losing
small stocks in the last quarter of the year but buy more small winners and small losers in the
subsequent quarter. They conclude that this trading pattern of institutions reflects investment
strategies that are consistent with window-dressing.
Meier and Schaumburg (2004) analyze the semiannual holdings and daily net asset values of
4,025 U.S. domestic equity mutual funds from 1997 to 2002. They compare the realized fund
13
return with a hypothetical buy-and-hold return that the fund would have earned had it held the
reported portfolio during the weeks leading up to the reporting date. The rationale for their
method is that the hypothetical holding-based return will outperform the realized return if the
trading due to window-dressing occurs over the last days of the quarter. Their empirical results
show that the hypothetical returns are higher than the realized returns for some funds and that
mutual funds with poor recent performance are more likely to window-dress.
Although previous studies provide evidence that is consistent with window-dressing
behavior of fund managers, they do not examine the effect of window-dressing on fund flows.
This paper fills in this blank by investigating the relation between fund flows and disclosed
portfolio holdings, which could be subject to the unobserved window-dressing strategy.
3. Data
3.1. Data source
We create the main data set by merging the survivorship-bias-free mutual fund database
from the Center for Research in Security Prices (CRSP) with the Thomson Financial mutual fund
holding database and the CRSP stock database. The CRSP mutual fund database includes
information on mutual fund monthly return, total net assets, inception date, fee structure, fund
investment objective, asset turnover ratio, and other fund attributes. The Thomson Financial
mutual fund database provides quarterly or semiannual holdings of most U.S. equity mutual funds.
We merge these two databases using the MFLINKS database from Wharton Research Data
Services (WRDS).
We exclude the balanced, bond, index, international, and sector funds to focus on actively
managed equity funds that invest mainly in the U.S. stock market. We also exclude funds that are
closed to new investors. We use the Wiesenberger (WI) fund type code, the ICDI fund objective
code, and Standard & Poor’s detailed objective code to categorize funds as Growth, Growth and
14
Income, and Income funds.3 One fund may have multiple share classes. Weighting each share
class by its total net assets, we obtain the value-weighted averages of monthly and thereafter
quarterly net return, expense ratio, turnover ratio, and total loads at the fund level. The total net
assets of the fund equals the summation of total net assets of each share class.
We link individual stocks in fund portfolio to the CRSP stock database to find the stock
performance over the preceding three months up to the last trading date of the quarter. We delete
the holdings on funds, ADRs, bonds, foreign stocks, and preferred stocks, and exclude those
reported portfolios that have less than 70% of the fund’s assets invested in common stocks. Some
holding stocks have missing prices or lack entries for the number of holding shares, and as a
result we cannot determine their weights in portfolio. We discard a quarterly report if the number
of missing-weight stocks over the number of all common stocks in portfolio yields a ratio larger
than 1%. The final sample is composed of 27,286 quarterly reports from 2,336 equity funds that
cover the period from March 1980 through December 2005.
Following Lakonishok et al. (1991) and He, Ng, and Wang (2004), at the end of each quarter
we sort in descending order all domestic stocks in the CRSP into quintiles based on their returns
over the past three months. The first quintile consists of stocks that achieve the highest returns.
For each portfolio report, we identify stocks that belong to different return quintiles and then
calculate the proportion of the fund’s assets invested in the first and fifth quintile, respectively.
We refer to these two proportions as the winner proportion and loser proportion.
We calculate monthly net fund flows as
TNAt − TNAt −1 ⋅ (1 + rt ) ,
3
The Wiesenberger Fund Type Code (WI) is available through 1993. The ICDI Fund Objective Code
(ICDI) is available from 1993 through July 2003. Standard &Poor’s detailed objective code (S&P) begins
in 1993, and formerly was the Strategic Insight Objective code. We categorize as “Growth” those funds
with the WI code of SCG, AGG, G, LTG, MCG, G-S, S-G, and GRO, funds with the ICDI code of AG,
AGG, and LG, and funds with the S&P code of SCG, AGG, and GRO. We categorize as “Growth and
Income” those funds with the WI code of GCI, G-I, G-I-S, G-S-I, I-S-G, S-G-I, S-I-G, and GR, funds with
the ICDI code of GI and TR, and funds with the S&P code of GRI, ING, and GMC. We categorize as
“Income” those funds with the WI code of I, I-S, IEQ, and ING, funds with the ICDI code of IN, and funds
with the S&P code of ING as “Income”.
15
where TNA is the total net assets of the fund at the end of the month and rt is the net return at
month t. Quarterly fund flows are the summation of fund flows in the three consecutive months of
the quarter.
3.2. Descriptive statistics
Table 1 presents descriptive statistics of the main variables used in analysis. The median
(mean) of quarterly net fund flows is -0.23 (5.28) millions. The winner proportion has a median
(mean) of 15.6% (17.4%) while the loser proportion has a median (mean) of 10.3% (11.1%). The
data indicates that more assets are invested in winners than losers in the reported portfolios.
Correlation coefficients between variables are shown in Table 2. The winner proportion and
loser proportion are negatively correlated, -0.20. This finding is conceivable because more
investment in winners will lead to less investment in losers, given a fixed amount of fund assets.
The correlation coefficient between the winner proportion and quarterly fund return is 0.19,
which is consistent with the notion that a fund should have achieved good performance if it has a
large proportion of the assets invested in winning stocks. The correlation between the loser
proportion and quarterly fund return is -0.02.
4. The window-dressing measure
Without a time series data of a fund’s daily holdings, fund investors do not know for sure
that the manager has engaged in window-dressing. However, using all available public
information, investors can infer the likelihood that window-dressing has occurred. Several
financial service providers such as Yahoo!Finance and Morningstar provide easily accessible
information such as monthly fund returns and top5 or top10 holdings of a fund. The SEC’s Edgar
database even provides for free the complete portfolio holdings reported by fund managers. Based
16
on this public information, we construct a measure that indicates the likelihood that windowdressing has occurred.
4.1. Variable construction
For each quarter and each fund sector (Growth, Growth and Income, and Income), we sort
funds in descending order by quarterly return and find their percentile rank of return, with funds
in the first percentile being the best performing funds and funds in the 100th percentile being the
worst. Then, we find their percentile rank of winner proportion, with funds in the first percentile
having the highest winner proportion and funds in the 100th percentile having the lowest.
Similarly, we sort funds in ascending order by loser proportion, with funds in the first percentile
having the lowest loser proportion and funds in the 100th percentile having the highest. After
these three independent sortings, we obtain the percentile rank of fund performance, the
percentile rank of winner proportion, and the percentile rank of loser proportion for each fund.
In the absence of window-dressing, a well performing fund should have a high percentile
rank of fund performance, a high percentile rank of winner proportion, and a high percentile rank
of loser proportion. On the contrary, a poorly performing fund should have a low percentile rank
of fund performance, a low percentile rank of winner proportion, and a low percentile rank of
loser proportion. These relationships are shown in the Appendix. If a fund has a low percentile
rank of performance but relatively high percentile ranks of winner and loser proportions, this rank
inconsistency suggests that the fund manager may has engaged in window-dressing. The larger
the rank inconsistency, the higher the probability that window-dressing has occurred. We define
the rank gap measure for window-dressing, WD, as
PerformanceRank −
WinnerRank + LoserRank
,
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile
rank of winner proportion, and LoserRank is the percentile rank of loser proportion. The
17
theoretical bound of rank gap is [-99, 99], while we find that the median (mean) of this measure is
–1 (-0.0029) and its range is [-96.5, 99].
4.2. Trading activity
In this section, we investigate the relation between the rank gap measure and managers’
trading activity. Window-dressing involves unnecessary trading activities that buy winners and
sell losers prior to the end of the quarter. Thus, a window-dresser would trade more than he does
in the absence of window-dressing. If our measure catches the window-dressing behavior, we
should observe a positive relation between this measure and the trade volume (in dollars) of the
contemporary quarter.
The Thomson Financial database reports net changes in shares since prior reports. Using
these share change data we calculate trade volume scaled by the total net assets for each net share
change. We obtain the total trade volume for a given quarter by adding up all individual trade
volume, as window-dressing involves both buying winners and selling losers.4 Then we estimate
an OLS regression model of quarterly trade volume on contemporary rank gap, controlling for
fund performance and other fund characteristics.
TradeVolum ei ,t = α + β 1WDi ,t + ψΧ i ,t + ε i ,t ,
(1)
where X is a vector of control variable that includes fund performance, size, loads, expense ratio,
age, flows, and dummies for investment objective, fund, and year. The standard errors are robust
to heteroskedasticity and are clustered at the fund level.
The results reported in Table 3 indicate a positive relation between the rank gap measure and
trading activity of the current quarter. In model 1 where funds are evaluated on quarterly return,
the coefficient of rank gap is 0.0005 with the 1% significance level. Higher past return is
associated with higher trading activity. Larger fund size leads to lower trading activity, a causality
4
We recognize that this “trade volume” overlooks the interim trading.
18
that could be traced to the less flexibility in changing portfolio holdings. When funds are
evaluated on their returns over the past 12 months, we obtain very close results reported in
regression model 2.
It is very likely that after the reporting date a window-dressing manager will rebalance his
portfolio and shift back to the original portfolio before window-dressing. In that case, there will
be additional trading in the subsequent quarter. To test the relation between the rank gap measure
and trading activity in the following period, we estimate a regression model of quarterly trade
volume on lagged rank gap, while controlling for other fund characteristics.
TradeVolum ei ,t = α + β 1WDi ,t −1 + ψΧ i ,t −1 + ε i ,t ,
(2)
where X is a vector of control variable that includes lagged fund performance, size, loads,
expense ratio, age, flows, and dummies for investment objective, fund, and year. The regression
results summarized in Table 4 show that higher rank gap leads to higher trade volume in the
subsequent quarter. The coefficients of rank gap in model 1 and model 2 are 0.0208 and 0.0152,
respectively, and both are statistically significant at the 1% level.
Overall, the findings on trade volume in both contemporary and subsequent quarters are
consistent with the conventional understanding of window-dressing that this strategy involves
higher trading activities than in the absence of window-dressing.
4.3. Momentum strategy
Fund managers who embark on a momentum strategy will buy winners and sell off losers
when adjusting their portfolios. A fund that window-dresses and another fund that pursues a
momentum strategy can exhibit similar allocation of assets. That is, more investment in winners
than losers. If our rank gap measure is unable to discriminate between a window-dressing and
momentum strategy, its viability to detect window-dressing may be called into question.
19
Consequently, we test the measure to ensure that it is a good proxy for the window-dressing
behavior rather than the momentum strategy.
Jegadeesh and Titman (1993) compare 16 momentum strategies that select stocks based on
their returns over the past one, two, three, and four quarters and hold portfolios for periods that
vary from one to four quarters. They refer to a strategy that selects stocks based on their returns
over the past J months and holds them for K months as a J-month/K-month strategy. Their results
show that all those portfolio returns are statistically significant except for the three-month/threemonth strategy. Four portfolios that select stocks based on their returns over the past three months
obtain the lowest returns among the 16 strategies. Keeping the three-month holding period
constant, the momentum profits increase as J increases. Among the 16 strategies, the most
successful one is the 12-month/three-month strategy.
Since our window-dressing measure is constructed based on stock performance over the past
three months and recalculated every three months, it may catch the three-month/three-month
momentum strategy if mutual fund managers indeed adopt this particular strategy that selects
stocks based on their returns over the past three months and holds them for one quarter.
Nevertheless, fund managers should not have incentives to employ such a momentum strategy
because, as showed in Jagadeesh and Titman (1993), this strategy does not produce momentum
returns. Therefore, the rank gap measure constructed from empirical data can not happen to be a
proxy for a “momentum strategy” that was unlikely to be used by mutual fund managers.
The extant literature finds strong evidence that the momentum strategy is associated with
higher returns in the following periods (see, e.g., Jegadeesh and Titman, 1993; Carhart, 1997;
Sias, 2007). Accordingly, if rank gap catches the momentum strategy, there should be a positive
relation between this measure and fund performance in the next quarter. To test this conjecture,
we estimate a regression model of quarter fund return on lagged rank gap while controlling for
fund performance and other pertinent characteristics.
20
Re turn i ,t = α + β 1WDi ,t −1 + ψ Χ i ,t −1 + ε i ,t
(3)
Table 5 summarizes the regression results. In model 1 where funds are evaluated by their
quarterly performance, the coefficient of rank gap is -0.0006 and statistically significant at the 1%
level. It indicates that a larger rank gap will lower fund performance in the next quarter, which is
inconsistent with the nature of the momentum strategy. On the contrary, this evidence is
consistent with the conventional notion that window-dressing destroys value and drags down fund
performance mainly because of additional trading costs. Similar results are found in model 2
where funds are evaluated by their performance over the past 12 months up to the last date of the
quarter.5
The unnecessary trading involved in window-dressing incurs additional transaction costs,
which would also drag down performance of the quarter-ending month. We estimate a regression
model of quarter-ending month return on rank gap and find a negative relation. This unreported
evidence reaffirms the previous finding that window-dressing destroys fund value.
A manager that pursues a momentum strategy will always buy winners and sell off losers,
regardless of past fund performance. As a result, a negative relation between past fund
performance and a proxy for the momentum strategy is unlikely to occur. In contrast, prior
studies such as He, Ng, and Wang (2004) and Meier and Schaumburg (2004) find that poorly
performing funds are more likely to window-dress. To further investigate whether our measure is
a reasonable proxy for window-dressing, we perform a multivariate analysis on the relation
between rank gap and past fund performance.
Considering managers may have extraordinary incentive to window-dress if their
performance is extremely poor compared to their peers, we estimate a quadratic relation between
window-dressing and past fund performance. We rank funds into quintiles based on quarterly
(annual) returns and group the three middle quintiles together. Funds belonging to the fifth
5
In a robustness test, we observe a negative relation between rank gap and fund return in the successive
month.
21
quintile are the best performing funds. Then we create two dummies, r_q234 and r_q5, for funds
located in the middle quintiles and the fifth quintile, respectively. We estimate the following
regression model,
WDi ,t = α + β 1 r _ q 234 i ,t + β 2 r _ q5 i ,t + ψ Χ i ,t + ε i ,t .
(4)
Table 6 reports the results. In model 1, funds are ranked by quarterly returns. The estimate of
the coefficient of performance dummy for middle quintiles is -24.6419 while that of the fifth
quintile is -49.8833. Both estimates are statistically significant at the 1% level. Model 2 uses
ranks of past annual performance and generates consistent results. The negative relation between
past fund performance and the rank gap measure is consistent with He, Ng, and Wang (2004) and
Meier and Schaumburg (2004) in that poorly performing funds are more likely to window-dress.
In summary, the findings in prior studies and the new evidence shown above indicate that
the rank gap measure is inconsistent with the momentum strategy and that it is a reasonable proxy
for the unobserved window-dressing strategy employed by mutual fund managers to promote
fund flows.
5.
Fund flows
5.1. Window-dressing and fund flows
In this section we investigate the effect of window-dressing on fund flows in subsequent
quarters. We estimate the following regression model,
Flows i ,t = α + β 1WDi ,t −1 + β 2WDi ,t − 2 + ψΧ i ,t −1 + ε i ,t ,
(5)
where Flows is quarterly fund flows measured in millions of U.S. dollars; X is a vector of control
variable that includes lagged fund performance, size, loads, expense ratio, turnover, age, flows in
the prior quarter, and dummies for investment objective, fund, and year.
The regression results of model 1 and model 2 reported in Table 7 indicate a negative
relation between the rank gap measure and fund flows in subsequent quarters. In model 1, funds
22
are evaluated and ranked by quarterly returns. The coefficient of rank gap in the last quarter is 0.0505 at the 5% significance level while that for the second-last quarter is -0.1556 at the 1%
significance level. The coefficient of the middle quintiles in performance rank is 3.7884 while
that of the fifth quintile is 8.3257, and both are statistically significant at the 1% level. This
convexity between performance and flows is consistent with the extant literature (see, e.g.,
Ippolito, 1992; Chevalier and Ellison, 1997; Sirri and Tufano, 1998). These results are robust
when funds are valuated by annual returns, as shown in model 2. It is evident that fund investors
infer managers’ window-dressing behavior and reduce their investment if they suspect windowdressing has occurred. 6
We examine the multicollinearity between independent variables and find that all variables
(excluding sector dummy, fund dummy, and year dummy) have a variance inflation factor (VIF)
below two, which is much lower than the critical value of 10. This finding suggests that the
negative relation between window-dressing and fund flows is not driven by the negative relation
between performance and flows.
The negative response of fund flows to window-dressing behavior of managers is
conceivable. Window-dressing involves unnecessary trading activities that are costly. Funds incur
both explicit and implicit trading costs such as brokerage commissions and price impact. These
transaction costs will drag down the net returns to investors because the Net Asset Value (NAV)
of a fund is calculated after the deduction of all costs. In addition, the portfolio composition
subject to window-dressing can mislead investors when they make investment decisions. As a
result, window-dressing incurs high agency costs without adding any value for fund investors.
Because window-dressing is contrary to the best interests of fund investors, investors will respond
6
We also estimate a quadratic relation between rank gap and fund flows and find supportive evidence.
Since the quadratic performance-flows relation exhibits a deeper slope in higher returns while the quadratic
relation between rank gap and flows shows a deeper slope in lower returns, this difference implies that the
negative relation between rank gap and flows is not because of performance.
23
negatively by reducing their investment in suspected funds that have exhibited high windowdressing likelihood.
5.3. Different flow sensitivity to lag1_WD and lag2_WD
One interesting finding that deserves more attention is that quarterly fund flows are less
sensitive to window-dressing in the immediately past quarter than to that in the second to last
quarter. Wald test indicates that the coefficients of lag1_WD and lag2_WD are different from
each other at the 1% significance level. We argue that the reason for this difference in flow
sensitivity lies in the fact that fund investors, in general, do not observe disclosed portfolio
holdings until typically two months after the end of the quarter.
Under the Investment Company Act of 1940, the SEC requires mutual fund managers file
their quarterly reports of portfolio holdings within 60 days after the end of a quarter. This rule
actually allows managers to file their reports with delay. To obtain a better idea of how much
fund managers delay their reports, we randomly choose 20 equity funds from Yahoo!Finance and
use the SEC’s Edgar database to find the time lag between the reporting date and the filing date.
We find that 19 of these randomly chosen funds filed their reports at least 50 days after the end of
the quarter and one fund filed its reports after a 40-day delay. We also examine the Thomson
Financial mutual fund holding database and find similar evidence that a large number of mutual
funds delay their reports.
Quarterly fund flows are the summation of flows in three successive months. Since investors
do not observe disclosed portfolio holdings until two months after the reporting date, the rank gap
measure can explain some variation of fund flows beginning in the third month of the subsequent
quarter, but not that in the first two months. During all three months of the subsequent second
quarter, more investors will have examined the disclosed portfolios and responded negatively to
suspected window-dressing behavior. Accordingly, we should observe a higher sensitivity of fund
flows to window-dressing in the second-last quarter. To test this hypothesis that only flows
24
occurred in the third month are sensitive to lag1_WD while flows in all three months are sensitive
to lag2_WD, we estimate such simultaneous equations,
Flows i ,t ,1 = α 1 + β 1WDi ,t −1 + β 2WDi ,t − 2 + ψΧ i ,t −1,1 + ε i ,t ,1
Flows i ,t , 2 = α 2 + β 1WDi ,t −1 + β 2WDi ,t − 2 + ψΧ i ,t −1, 2 + ε i ,t , 2
(6)
Flows i ,t ,3 = α 3 + β 1WDi ,t −1 + β 2WDi ,t − 2 + ψ Χ i ,t −1,3 + ε i ,t ,3
where Flows i ,t ,1 is fund i’s net flows in the first month of the quarter; Flows i ,t , 2 is flows in the
second month of the quarter; Flowsi ,t ,3 is flows in the third month of quarter t;. X is a vector of
control variables that include lagged fund performance, size, loads, expense ratio, turnover, age,
preceding monthly flows, and dummies for investment objective, fund, and year. We report the
regression results in Table 8.
It appears that flows that occurred in the first two months of the quarter are not sensitive to
lag1_WD while flows that occurred in the third month of the quarter exhibit strong sensitivity.
The coefficient of lag1_WD of the third-month flow model, -0.0493, is very close to that in
model 1 of Table 7, -0.0505. Furthermore, fund flows in all three successive months are sensitive
to lag2_WD. This evidence is consistent with our hypothesis that investors do not observe
disclosed portfolio holdings and therefore infer window-dressing until about two months later
after the end of the quarter. This evidence suggests that our rank gap measure is a good proxy for
window-dressing.
5.4. Incentives to window-dress
Compensations to mutual fund managers are linked to fund size. Therefore, managers have
strong incentive to retain and attract assets under management. It is said that the reason for fund
managers to window-dress is to please current investors and attract new money. However, we
find that fund flows are negatively related to window-dressing. Does it mean mutual fund
25
window-dressing is an irrational behavior? We propose two reasons for the adoption of windowdressing by some fund managers.
Firstly, window-dressing may successfully allure some investors, especially those who are
not well investment-educated and who do not realize the existence of window-dressing. Less
complicated investors are more likely to be attracted by mutual funds’ top 5 or top 10 holdings,
which could be manipulated with window-dressing.
Second, poorly performing managers could benefit from window-dressing with delayed
reports. As mentioned earlier, a large number of fund managers do not file their reports until
around 60 days later. If the manager of a poorly performing fund window-dresses and fund
performance improves for whatever reason in the subsequent quarter, it is hard for investors to
tell if this manager has engaged in window-dressing or he has stock selection skill as long as the
disclosed winners do not depreciate much. Fund investors are likely to believe that this manager
has stock selection skill because it is natural for investors to attribute improved fund performance
to the disclosed high proportion of assets invested in winning stocks. On the other hand, if this
unskilled manager experiences poor performance again in the following quarter, his windowdressing behavior will be detected. However, he has little to lose because he already faced a threat
of being replaced at the end of the year because of the poor performance observed in the
preceding quarter.
6.
Robustness
We repeat all multivariate analysis by estimating panel regression models with fixed effect
and random effect specifications. The results do not change much. We still find strong evidence
that rank gap is a reasonable measure for window-dressing and that there is a negative relation
between rank gap and fund flows.
There is a Tax-Loss Selling Hypothesis in the literature that investors will sell off losing
stocks at the fourth quarter to realize investment loss, which investors can use to offset capital
26
gains and therefore lower their personal tax liability. Managers are agents of fund investors and
therefore may embark on tax-loss selling on behalf of fund investors. To exclude the possibility
that our measure might catch this “tax-loss selling” behavior that occurs only at the fourth quarter,
we repeat all multivariate analysis using observations of the first three calendar quarters. Still, we
obtain very consistent results.
We construct a new variable, WD_dummy, that equals one if rank gap is positive and zero
otherwise. We estimate the regression model (1) to (6) with this alternative window-dressing
measure and obtain similar interpretation and conclusions. The results reported in Table 9
reaffirm that there is a negative relation between window-dressing and fund flows in subsequent
quarters.
Kacperczyk, Sialm, and Zheng (2006) estimate the impact of managers’ unobserved actions
on fund returns using return gap, the difference between a fund’s reported fund return and the
return of a hypothetical portfolio that invests in the fund’s disclosed end-of-period holdings. They
argue that this return gap measure captures the effect of multiple managerial actions including
interim trading, momentum strategies, and the pursuit of window-dressing behavior. If a manager
window-dresses, the reported return would under-perform the hypothetical return. Accordingly, a
negative return gap would suggests that window-dressing may have occurred. Thus, their measure
could be a proxy for window-dressing. To have a better understanding of the relation between our
measure and the return gap measure, we follow Kacperczyk et al. (2006) and compute the return
gap measure for the quarter-ending months.
Consistent with the findings in Kacperczyk et al. (2006), we find that the mean of the
hypothetical return of the quarter-ending month is 0.989%. If a fund has engaged in windowdressing near the end of the quarter, the hypothetical return would be higher than the reported
return leading to a negative return gap. Thus, there should be a negative correlation between the
return gap and rank gap measure if return gap contains some information of window-dressing and
if rank gap is a reasonable proxy for window-dressing. We find that the correlation coefficient
27
between rank gap and return gap is -0.15 with the 1% significance level. This observation
suggests that rank gap and return gap share some information regarding the likelihood of
unobserved window-dressing behavior.
Next, we test the relation between return gap and fund flows. Since a negative return gap
suggests that window-dressing may have occurred, we should observe a positive relation between
this measure and fund flows in the third month of the subsequent quarters. However, we should
not observe a relation between return gap and flows in the first and second month because
investors do not observe disclosed portfolio holdings until two months after the end of the quarter.
We estimate the regression model (6) using return gap as a proxy for window-dressing. The
regression results are summarized in Table 10. We observe that fund flows in the first month of a
quarter are positively related to return gap of the last quarter-ending month while flows in the
second and third month are not. This finding is inconsistent with the fact that investors do not
observe the disclosed portfolio holdings until about two-months later because managers delay
reports.
To further explore whether the rank gap measure provides information beyond that
contained in the return gap measure, we conduct a J-test for testing between non-nested
regression models.7 First, we estimate a regression model of the third-month flows on the rank
gap measure and calculate the set of fitted value for the dependent variable. Then, we estimate a
regression model of the third-month flows on the return gap measure and calculate the set of
fitted value for the dependent variable. Next, we estimate the rank gap model again, but also
using the fitted value obtained from the return gap model as an added explanatory variable. We
also estimate the return gap model again, but also using the fitted value obtained from the rank
gap model as an added explanatory variable. The null hypothesis is that the rank gap model fit the
data better than the model using the return gap measure. The null hypothesis is supported if the
estimate of the coefficient of the fitted value from the rank gap model is significantly different
7
Please see Davidson and MacKinnon (1981) and McAleer (1995) for a discussion of the J-test procedure.
28
from zero and the estimate of the coefficient of the fitted value from the return gap model is not
significant. If both estimates of the coefficient of the fitted value from the return gap model and
rank gap model are significantly different from zero, then each measure provides a degree of
information not found in the other measure and the null hypothesis is rejected. If both estimates
are insignificant, then the two measures provide similar information.
We present the J-test results in Table 11 in which we show the estimates of the coefficient of
the added fitted value. The estimate of the coefficient of the fitted value from the return gap
model is not statistically different from zero, while the estimate of the coefficient of the fitted
value from the rank gap model is statistically significant at the 1% level. It appears that the rank
gap measure provides information beyond that contained in the return gap measure.
7.
Conclusions
Exploring a sample of 27,286 quarterly reports of 2,336 actively managed U.S. equity funds,
this paper examines the window-dressing behavior of fund managers as a strategy to attract fund
flows. We construct a rank gap measure to detect the unobserved window-dressing behavior. The
rationale for this approach is that, on average, a poorly performing fund should have a high
proportion of its assets invested in losers but low proportion in winners. Thus, observing a poorly
performing fund with a high proportion of assets in winners and a low proportion in losers
suggests a greater probability that window-dressing has occurred. Several tests provide supportive
evidence that this rank gap measure is a reasonable proxy for the unobserved window-dressing
behavior of fund managers.
Window-dressing involves unnecessary trading activities that buy winners and sell losers
prior to the end of the quarter. Thus, a window-dresser would trade more than he does in the
absence of window-dressing. We find a positive relation between window-dressing and trade
volume of both contemporary and subsequent quarters. The unnecessary trading involved in
window-dressing incurs additional transaction costs such as brokerage commission and price
29
impact, which drags down fund performance. We find consistent evidence that window-dressing
destroys fund value.
Trading involved in window-dressing incurs high costs. In addition, the portfolio
composition subject to window-dressing can mislead investors when they make investment
decisions. As a result, window-dressing incurs high agency costs without adding any value for
fund investors. Because window-dressing is contrary to the best interests of fund investors,
investors will respond negatively by reducing their investment in suspected funds that have
exhibited high window-dressing likelihood. Consistent with this reasoning, the empirical analysis
shows that net fund flows in subsequent quarters are negatively related to the rank gap measure
after controlling for fund performance and other pertinent characteristics. This evidence suggests
that fund investors infer window-dressing and reduce their investment in suspected funds. These
findings indicate that on average the window-dressing strategy does not promote fund flows.
Our empirical findings also suggest that managers of poorly performing funds are more
likely to engage in window-dressing than managers of well performing funds. Managers of well
performing funds have low incentives to window-dress because they have earned good image and
do not want to be punished with reduced net fund flows. In contrast, managers of poorly
performing funds have high incentives to window-dress because they wish to influence investors’
perception of their stock selection skill. Many fund managers delay their quarterly report for
about two months and window-dressing managers benefit from this report-file lag. If a poor
performing manager window-dresses and fund performance improves over the next quarter, fund
investors may believe that this manager has stock selection skill because it is natural for investors
to attribute improved fund performance to the disclosed high proportion of assets invested in
winners. As a result, the manager could hide his type. Even if fund performance in the subsequent
quarter is poor again and thus his window-dressing behavior is identified, the manager has little to
lose because he already faced a threat of being replaced at the end of the year because of the poor
performance observed in the preceding quarter.
30
Appendix
This appendix explains the construction of the rank gap measure for window-dressing. For each quarter we
sort in descending order all domestic stocks in the CRSP into quintiles based on their quarterly returns.
Stocks in the first quintile are winning stocks and those in the fifth quintile are losing stocks. For each
quarter and each fund sector (Growth, Growth and Income, and Income), we sort funds in descending order
by quarterly return, with funds in the first percentile being the best performing funds. Then, we sort funds
in descending order based on winner proportion, which is the percentage of the assets invested in the
winning stocks for the quarter. Similarly, we sort funds in ascending order by loser proportion, which is the
percentage of the assets invested in the losing stocks for the quarter. After these three independent sortings,
we obtain the percentile rank of fund performance, the percentile rank of winner proportion, and the
percentile rank of loser proportion for each fund. We define the rank gap measure for window-dressing as
PerformanceRank −
WinnerRank + LoserRank
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. The theoretical bound of the
rank gap measure is [-99, 99]. A larger rank gap indicates a higher likelihood that window-dressing has
occurred.
Rank
1
2
3
.
.
.
.
98
99
100
Fund Performance
Winner Proportion
Loser Proportion
1 (best performance)
2
3
.
.
.
.
98
99
100 (worst performance)
1 (highest proportion)
2
3
.
.
.
.
98
99
100 (lowest proportion)
1 (lowest proportion)
2
3
.
.
.
.
98
99
100 (highest proportion)
31
References
Carhart, M.M., 1997. On persistence in Mutual Fund Performance. Journal of Finance 52, 57-82.
Carhart, M.M., Kaniel, R., Musto, D.K., Reed, A.V., 2002. Leaning for the tape: Evidence of
gaming behavior in equity mutual funds. Journal of Finance 58, 661-693.
Chevalier, J., Ellison, G., 1997. Risk taking by mutual funds as a response to incentives. Journal
of Political Economy 105, 1167-1200.
Cici, G., Gibson, S., Moussawi, R., 2006. For better or worse? Mutual funds in side-by-side
management relationships with hedge funds. Working paper, the Wharton School and the College
of William & Mary.
Davidson, R., MacKinon, J.G., 1981. Several tests for model specification in the presence of
alternative hypotheses. Econometrica 49, 781-793.
He, J., Ng, L., Wang, Q., 2004. Quarterly trading patterns of financial institutions. Journal of
Business 77, 493-509.
Ippolito, R.A., 1992. Consumer reaction to measures of poor quality: Evidence from the mutual
fund industry. Journal of Law and Economics 35, 45-70.
Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: implications for
stock market efficiency. Journal of Finance 48, 65-91.
Kacperczyk, M., Sialm, C., Zheng, Lu, 2006. Unobserved actions of mutual funds. Review of
Financial Studies, Advance Access, October.
Lakonishok, J., Shleifer, A., Thaler R., Vishny R., 1991. Window dressing by pension fund
managers. American Economic Review 81, 227-231.
McAleer, M., 1995. The significance of testing empirical on-nested models. Journal of
Econometrics 67, 149-171.
Meier, I., Schaumburg, E., 2004. Do funds window dress? Evidence for U.S. domestic equity
mutual funds. Unpublished working paper, HEC Montreal and Kellogg School of Management.
Morey, M.R., O’Neal, E.S., 2006. Window dressing in bond mutual funds. Journal of Financial
Research 29, 325-347.
Musto, D.K., 1997. Portfolio disclosure and year-end price shift. Journal of Finance 52, 15631588.
Musto, D.K., 1999. Investment decisions depend on portfolio disclosures. Journal of Finance 54,
935-952.
Ng, L., Wang, Q., 2004. Institutional trading and the turn-of-the-year effect. Journal of Financial
Economics 74, 343-366.
32
Sias, R.W., 2007. Causes and seasonality of momentum profits. Financial Analysts Journal 63,
48-54.
Sias, R.W., Starks, L.T., 1997. Institutions and individuals at the turn-of-the-year. Journal of
Finance 52, 1543-1562.
Sirri, E.R., Tufano, P., 1998. Costly search and mutual fund flows. Journal of Finance 53, 15891622.
33
Table 1
Summary Statistics for Mutual funds
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. Flow is the quarterly fund flows measured in millions of U.S. dollars.
Winner_prop is the proportion of the assets invested in winning stocks. Loser_prop is the proportion of the
assets invested in losing stocks. In each quarter we sort in descending order all domestic stocks in the
CRSP into quintiles based on their quarterly returns. Stocks in the first quintile are winning stocks and
those in the fifth quintile are losing stocks. quarter_return is the total return of the fund over a quarter. TNA
is the total net assets. Load is the total front-end, deterred and rear-end charges. Expense is the expense
ratio. Turnover is the annual asset turnover of the fund. Age is the number of years from the inception date
up to the end of the quarter. All variables are winsorized at one and the 99th percentile.
Variable
flow (million)
winner_prop (%)
loser_prop (%)
quarter_return (%)
TNA (million)
load (%)
expense (%)
turnover (%)
Age (year)
Median
-0.23
15.6
10.3
4.0
163
0.57
1.25
65
8
Mean
5.28
17.4
11.1
4.8
685
2.08
1.33
88
12.8
Std. Dev.
75.6
11.5
6.4
11.6
1575
2.42
0.46
80
13.7
Min
-270
0
0
-25.6
2
0
0.36
2
0.1
Max
440
52.7
31.8
42.5
11037
9.50
2.97
462
82.6
34
Table 2
Correlation Matrix
This table reports the Pearson correlation coefficient between main variables. The sample includes 27,286
quarterly reports from 2,336 funds that cover the time period from March 1980 through December 2005.
Flow is the quarterly fund flows measured in millions of U.S. dollars. Winner_prop is the proportion of the
assets invested in winning stocks. Loser_prop is the proportion of the assets invested in losing stocks. In
each quarter we sort in descending order all domestic stocks in the CRSP into quintiles based on their
quarterly returns. Stocks in the first quintile are winning stocks and those in the fifth quintile are losing
stocks. quarter_return is the total return of the fund over a quarter. LogTNA is the logarithm of (1+ total net
assets). Load is the total front-end, deterred and rear-end charges. Expense is the expense ratio. Turnover is
the annual asset turnover of the fund. LogAge is the logarithm of (1+ age). *, **, *** denote a significant
difference from zero at the 10%, 5%, and 1% levels, respectively.
flow
winner_prop
loser_prop
quarter_r
logTNA
load
expense
turnover
logAge
winner_prop loser_prop
quarter_r
logTNA
load
expense
turnover
0.06 ***
-0.02 ***
-0.20 ***
0.11 ***
0.19 ***
-0.02 ***
0.08 ***
-0.04 ***
-0.03 ***
-0.02 ***
-0.04 ***
-0.01
-0.03 ***
0.12 ***
-0.03 ***
-0.04 ***
0.06 ***
-0.04 ***
0.14 ***
0.08 ***
-0.02 ***
-0.36 ***
0.27 ***
0.03 ***
0.04 ***
-0.12 ***
-0.10 ***
-0.05 ***
-0.03 ***
0.49 ***
0.30 ***
-0.01 **
0.19 ***
0.22 ***
-0.23 ***
35
-0.12 ***
Table 3
Regression of trade volume on contemporary rank gap
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variable is quarterly trade volume in dollars scaled by total net
assets, which is obtained from net changes in holdings shares since the prior quarterly report. WD is the
rank gap measure for window-dressing defined as:
WinnerRank + LoserRank
PerformanceRank −
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. quarter_return is the total
return of the fund over the quarter. year-return is the total return of the fund over the past 12 months.
logTNA is the logarithm of (1+ total net assets). Expense is the expense ratio. Load is the total front-end,
deterred and rear-end charges. LogAge is the logarithm of (1+ age). Flow is the quarterly fund flows
measured in millions of U.S. dollars. p-value is reported under the coefficients. *, **, *** denote a
significant difference from zero at the 10%, 5%, and 1% levels, respectively.
Variable
WD
quarter_return
Model 1
0.0005
0.00
0.0010
0.00
***
load
expense
logAge
flow
sector dummy
fund dummy
year dummy
Adjusted R2
observation
-0.0264
0.00
0.0036
0.13
-0.0033
0.79
-0.0590
0.00
0.0001
0.02
Yes
Yes
Yes
0.38
24433
***
***
year_return
logTNA
Model 2
0.0004
0.00
***
***
**
0.0002
0.00
-0.0263
0.00
0.0036
0.129
-0.0025
0.84
-0.0574
0.00
0.0001
0.03
***
***
***
**
Yes
Yes
Yes
0.38
24433
36
Table 4
Regression of trade volume on lagged rank gap
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variable is quarterly trade volume in dollars scaled by total net
assets, which is obtained from net changes in holdings shares since the prior quarterly report. WD is the
rank gap measure for window-dressing defined as:
WinnerRank + LoserRank
PerformanceRank −
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. quarter_return is the total
return of the fund over the quarter. year-return is the total return of the fund over the past 12 months.
logTNA is the logarithm of (1+ total net assets). Expense is the expense ratio. Load is the total front-end,
deterred and rear-end charges. LogAge is the logarithm of (1+ age). Flow is the quarterly fund flows
measured in millions of U.S. dollars. All control variables are lagged for one period. p-value is reported
under the coefficients. *, **, *** denote a significant difference from zero at the 10%, 5%, and 1% levels,
respectively.
Variable
lag1_WD
lag1_quarter_return
Model 1
0.0208
0.00
0.0198
0.18
***
lag1_year_return
lag1_logTNA
lag1_load
lag1_expense
lag1_logAge
lag1_flow
sector dummy
fund dummy
year dummy
Adjusted R2
observation
-0.9745
0.00
0.0729
0.73
1.6789
0.14
1.7991
0.06
0.0053
0.65
Yes
Yes
Yes
0.14
23244
***
*
Model 2
0.0152
0.01
-0.0183
0.13
-0.8893
0.00
0.0789
0.70
1.7545
0.12
1.8395
0.06
0.0073
0.55
***
***
*
Yes
Yes
Yes
0.14
23244
37
Table 5
Regression of funds’ quarterly return on lagged rank gap
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variable is the total return of the fund over the quarter. WD is the
rank gap measure for window-dressing defined as:
WinnerRank + LoserRank
PerformanceRank −
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. quarter_return is the total
return of the fund over the quarter. year-return is the total return of the fund over the past 12 months.
logTNA is the logarithm of (1+ total net assets). Load is the total front-end, deterred and rear-end charges.
Expense is the expense ratio. Turnover is the annual asset turnover of the fund. LogAge is the logarithm of
(1+ age). Flow is the quarterly fund flows measured in millions of U.S. dollars. All control variables are
lagged for one period. p-value is reported under the coefficients. *, **, *** denote a significant difference
from zero at the 10%, 5%, and 1% levels, respectively.
Variable
lag1_WD
lag1_quarter_return
Model 1
-0.0006
0.00
-0.0022
0.00
***
lag1_load
lag1_expense
lag1_turnover
lag1_logAge
lag1_flow
sector dummy
fund dummy
year dummy
Adjusted R2
observation
-0.0114
0.00
0.0008
0.35
-0.0019
0.66
0.0001
0.00
0.0141
0.00
0.0001
0.00
Yes
Yes
Yes
0.29
27069
***
***
lag1_year_return
lag1_logTNA
Model 2
-0.0003
0.00
***
***
***
***
-0.0004
0.00
-0.0120
0.00
0.0008
0.30
-0.0035
0.40
0.0001
0.00
0.0110
0.00
0.0001
0.00
***
***
***
***
***
Yes
Yes
Yes
0.25
27069
38
Table 6
Regression of rank gap on fund return
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variable is the rank gap measure for window-dressing defined as:
WinnerRank + LoserRank
PerformanceRank −
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. We rank funds in ascending
order into quintiles based on quarterly return and group the three middle quintiles together. quarter_q234
and quarter_r_q5 are dummies for funds located in the middle quintiles and the fifth quintile, respectively.
Similarly, year_r_q234 and year_r_q5 are dummies for funds located in the middle quintiles and the fifth
quintile when funds are ranked based on annual return. logTNA is the logarithm of (1+ total net assets).
Load is the total front-end, deterred and rear-end charges. Expense is the expense ratio. Turnover is the
annual asset turnover of the fund. LogAge is the logarithm of (1+ age). Flow is the quarterly fund flows
measured in millions of U.S. dollars. p-value is reported under the coefficients. *, **, *** denote a
significant difference from zero at the 10%, 5%, and 1% levels, respectively.
Variable
quarter_r_q234
quarter_r_q5
Model 1
-24.6419
0.00
-49.8833
0.00
Model 2
***
***
year_r_q234
year_r_q5
logTNA
load
expense
turnover
logAge
flow
sector dummy
fund dummy
year dummy
Adjusted R2
observation
-0.4658
0.08
0.0118
0.96
3.1248
0.00
0.0268
0.00
2.1788
0.01
-0.0381
0.00
Yes
Yes
Yes
0.44
26868
*
***
***
***
***
-14.2147
0.00
-28.0951
0.00
0.7545
0.01
-0.1069
0.67
4.5943
0.00
0.0213
0.00
2.2693
0.02
-0.0507
0.00
***
***
***
***
***
**
***
Yes
Yes
Yes
0.20
26868
39
Table 7
Regression of quarterly flows on rank gap
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variable is quarterly fund flows measured in millions of U.S.
dollars. WD is the rank gap measure for window-dressing defined as:
WinnerRank + LoserRank
PerformanceRank −
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. We rank funds based on
quarterly return in ascending order into quintiles and group the three middle quintiles together.
quarter_q234 and quarter_r_q5 are dummies for funds located in the middle quintiles and the fifth quintile,
respectively. Similarly, year_r_q234 and year_r_q5 are dummies for funds located in the middle quintiles
and the fifth quintile when funds are ranked based on annual return. logTNA is the logarithm of (1+ total
net assets). Load is the total front-end, deterred and rear-end charges. Expense is the expense ratio.
Turnover is the annual asset turnover of the fund. LogAge is the logarithm of (1+ age). Flow is the
quarterly fund flows measured in millions of U.S. dollars. All control variables are lagged for one period.
p-value is reported under the coefficients. *, **, *** denote a significant difference from zero at the 10%,
5%, and 1% levels, respectively.
Variable
Model 1
lag1_WD
-0.0505
Mode 2
**
-0.0464 **
***
-0.1125 ***
0.04
lag2_WD
-0.1556
lag1_quarter_r_q234
3.7884
0.02
0.00
0.00
***
0.00
lag1_quarter_r_q5
8.3257
***
0.00
lag1_year_r_q234
5.9100
***
0.00
lag1_year_r_q5
19.1683 ***
0.00
lag1_logTNA
1.2956
lag1_load
2.3526
0.8488
0.44
0.62
**
2.1547
0.02
0.03
lag1_expense
-0.3624
-0.3756
lag1_turnover
-0.0238
0.05
0.05
lag1_logAge
-0.8881
-0.1778
lag1_flow
1.5625
0.91
0.90
**
0.84
0.00
**
-0.0239 **
0.97
***
1.5437
***
0.00
sector dummy
Yes
Yes
fund dummy
Yes
Yes
year dummy
Adjusted R2
Yes
Yes
0.51
0.52
observation
16006
16006
40
Table 8
Simultaneous equations of monthly flows on rank gap
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variables are monthly fund flows in the first, second, and third
month of the quarter and are measured in millions of U.S. dollars. WD is the rank gap measure for windowdressing defined as:
WinnerRank + LoserRank
PerformanceRank −
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. We rank funds based on
quarterly return in ascending order into quintiles and group the three middle quintiles together.
quarter_q234 and quarter_r_q5 are dummies for funds located in the middle quintiles and the fifth quintile,
respectively. Similarly, year_r_q234 and year_r_q5 are dummies for funds located in the middle quintiles
and the fifth quintile when funds are ranked based on annual return. logTNA is the logarithm of (1+ total
net assets). Load is the total front-end, deterred and rear-end charges. Expense is the expense ratio.
Turnover is the annual asset turnover of the fund. LogAge is the logarithm of (1+ age). Flow is monthly
fund flows measured in millions of U.S. dollars. All control variables are lagged for one period. p-value is
reported under the coefficients. *, **, *** denote a significant difference from zero at the 10%, 5%, and 1%
levels, respectively.
Variable
lag1_WD
lag2_WD
lag1_quarter_r_q234
lag1_quarter_r_q5
lag1_logTNA
lag1_load
lag1_expense
lag1_turnover
lag1_logAge
lag1_flow
sector dummy
fund dummy
year dummy
2
Adjusted R
observation
1st-month flow
0.0075
0.75
-0.0452
0.02
2.7932
0.04
4.6910
0.01
1.1579
0.00
0.2245
0.31
-1.1141
0.39
-0.0028
0.66
-0.0517
0.94
0.9981
0.00
Yes
Yes
Yes
0.22
16006
2nd-month flow 3rd-month flow
0.0031
-0.0493 **
0.90
0.028
**
-0.0664 ***
-0.0414 **
0.00
0.02
**
2.1992
1.1004
0.11
0.39
***
6.9297 ***
3.2723 *
0.00
0.07
***
0.6698 **
0.3839
0.05
0.23
-0.1505
-0.0390
0.50
0.85
2.3249 *
2.0032
0.08
0.11
0.0056
-0.0117 *
0.39
0.06
-1.3907 **
-1.1219 *
0.05
0.10
***
0.5501 ***
0.6545 ***
0.00
0.00
Yes
Yes
Yes
0.16
16006
Yes
Yes
Yes
0.36
16006
41
Table 9
Simultaneous equations of monthly flows on rank gap dummy
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variables are monthly fund flows in the first, second, and third
month of the quarter and are measured in millions of U.S. dollars. WD_dummy equals 1 when WD is
larger than zero and zero otherwise. WD is the rank gap measure for window-dressing defined as:
WinnerRank + LoserRank
PerformanceRank −
2
where PerformanceRank is the percentile rank of fund performance, WinnerRank is the percentile rank of
winner proportion, and LoserRank is the percentile rank of loser proportion. We rank funds based on
quarterly return in ascending order into quintiles and group the three middle quintiles together.
quarter_q234 and quarter_r_q5 are dummies for funds located in the middle quintiles and the fifth quintile,
respectively. Similarly, year_r_q234 and year_r_q5 are dummies for funds located in the middle quintiles
and the fifth quintile when funds are ranked based on annual return. logTNA is the logarithm of (1+ total
net assets). Load is the total front-end, deterred and rear-end charges. Expense is the expense ratio.
Turnover is the annual asset turnover of the fund. LogAge is the logarithm of (1+ age). Flow is the
quarterly fund flows measured in millions of U.S. dollars. All control variables are lagged for one period.
p-value is reported under the coefficients. *, **, *** denote a significant difference from zero at the 10%,
5%, and 1% levels, respectively.
Variable
lag1_WD_dummy
lag2_WD_dummy
lag1_quarter_r_q234
lag1_quarter_r_q5
lag1_logTNA
lag1_load
lag1_expense
lag1_turnover
lag1_logAge
lag1_flow
sector dummy
fund dummy
year dummy
2
Adjusted R
observation
1st-month flow
2nd-month flow
-1.3604
-1.4991
0.23
0.19
-3.1213
***
-2.5767 ***
0.00
0.01
1.9083
1.4753
0.14
0.26
3.0210
*
5.5812 ***
0.09
0.00
1.1362
***
0.6762 **
0.00
0.04
0.2273
-0.1498
0.31
0.50
-1.0001
2.3602 *
0.44
0.07
-0.0023
0.0051
0.72
0.43
0.0279
-1.3811 **
0.97
0.05
0.9961
***
0.5501 ***
0.00
0.00
Yes
Yes
Yes
0.22
16006
Yes
Yes
Yes
0.16
16006
3rd-month flow
-2.8179 ***
0.01
-1.6497 *
0.07
1.1278
0.36
3.3745 **
0.05
0.3883
0.22
-0.0341
0.87
1.9693
0.11
-0.0132 **
0.03
-1.1325 *
0.09
0.6545 ***
0.00
Yes
Yes
Yes
0.35
16006
42
Table 10
Simultaneous equations of monthly flows on return gap
The sample includes 27,286 quarterly reports from 2,336 funds that cover the time period from March 1980
through December 2005. The dependent variables are monthly fund flows in the first, second, and third
month of the quarter and are measured in millions of U.S. dollars. return_gap is the difference between the
realized fund return and the return of a portfolio that invests in the disclosed fund holdings from the
beginning of the quarter-ending month. We rank funds based on quarterly return in ascending order into
quintiles and group the three middle quintiles together. quarter_q234 and quarter_r_q5 are dummies for
funds located in the middle quintiles and the fifth quintile, respectively. Similarly, year_r_q234 and
year_r_q5 are dummies for funds located in the middle quintiles and the fifth quintile when funds are
ranked based on annual return. logTNA is the logarithm of (1+ total net assets). Load is the total front-end,
deterred and rear-end charges. Expense is the expense ratio. Turnover is the annual asset turnover of the
fund. LogAge is the logarithm of (1+ age). Flow is the quarterly fund flows measured in millions of U.S.
dollars. All control variables are lagged for one period. p-value is reported under the coefficients. *, **, ***
denote a significant difference from zero at the 10%, 5%, and 1% levels, respectively.
Variable
lag1_return_gap
lag2_return_gap
lag1_quarter_r_q234
lag1_quarter_r_q5
lag1_logTNA
lag1_load
lag1_expense
lag1_turnover
lag1_logAge
lag1_flow
sector dummy
fund dummy
year dummy
2
Adjusted R
observation
1st-month flow
0.3441
0.04
0.0831
0.61
2.1817
0.02
4.5720
0.00
1.2970
0.00
-0.0134
0.94
-0.5683
0.54
0.0008
0.86
-0.1594
0.75
0.8956
0.00
Yes
Yes
Yes
0.23
24967
**
**
***
***
***
2nd-month flow
-0.0806
0.69
0.3573 *
0.06
3.1901 ***
0.00
5.5983 ***
0.00
0.4533
0.11
-0.1669
0.38
1.2621
0.25
-0.0021
0.70
-0.8966
0.13
0.5358 ***
0.00
3rd-month flow
0.1951
0.263
0.3957 **
0.02
3.4012 ***
0.00
8.7509 ***
0.00
0.5536 **
0.03
0.0473
0.78
1.7732 *
0.07
-0.0112 **
0.02
-2.1764 ***
0.00
0.4626 ***
0.00
Yes
Yes
Yes
0.12
24967
Yes
Yes
Yes
0.22
24967
43
Table 11
J-test result
This table presents the J-test results of the monthly flow regression model using the rank gap measure vs.
regression model using the return gap measure. First, we estimate a regression model of flows in the third
month of the quarter on the rank gap measure and calculate the set of fitted value for the dependent variable.
Then, we estimate a regression model of the third-month flows on the return gap measure and calculate the
set of fitted value for the dependent variable. Next, we estimate the rank gap model again, but also using
the fitted value obtained from the return gap model as an added explanatory variable. We also estimate the
return gap model again, but also using the fitted value obtained from the rank gap model as an added
explanatory variable. We present the coefficient of the added fitted value. p-value is reported under the
coefficients. *, **, *** denote a significant difference from zero at the 10%, 5%, and 1% levels,
respectively.
variable
fitted value from return gap model
fitted value from rank gap model
rank gap model
return gap model
0.0465
0.97
1.0112
0.01
***
44
A Life Cycle Analysis of Performance and Growth
in U.S. Mutual Funds
Leng Ling*
Georgia State University
This version: June 3, 2008
Abstract
I propose a five-stage growth model to describe the life cycle evolution of mutual funds and
show that mutual funds exhibit distinctive performance, size, expense ratios, asset turnover, and
other pertinent characteristics through stages of incubation, high-growth, low-growth, maturity,
and decline. I also investigate the viability of managerial strategies to affect a fund’s life cycle
evolution and find that changing a declining fund’s investment objective is effective in
rejuvenating asset growth and thus repositioning the fund to younger life cycle stages. However,
the strategy of adding portfolio managers appears to have no such rejuvenation effect.
JEL Classification: G11; G20; L2; L22
Keywords: Mutual funds; Life cycle; Economies of scale; Managerial behavior; Growth
* I am grateful to my dissertation committee members, Gerald D. Gay (co-chair), Jason T. Greene (cochair), Conrad S. Ciccotello, and Harley E. Ryan for their invaluable advice and continued support. I thank
Vikas Agarwal, Marcin Kacperczyk, Jayant Kale, Jason Karceski, Yee Cheng Loon, Reza S. Mahani, Jame
E. Owers, Laura Starks, Ling Ling Wang, and seminar participants at Georgia State University, University
of Wisconsin at Whitewater, Bryant University, State University of New York at Albany, Slippery Rock
University, Georgia College & State University, and the 2007 Financial Management Association
Conference for their helpful comments and suggestions. Any errors that remain are mine. Contact
information: Department of Finance, J. Mack Robinson College of Business, Georgia State University,
Atlanta, GA 30303-3083. Tel.: 1-404-413-7314; Fax: 1-404-413-7312. E-mail address: [email protected].
45
1. Introduction
The aim of this study is to examine the mutual fund industry using a life cycle framework for
purpose of investigating whether fund’s life cycle is systematically associated with observed
variations in performance, flows, strategies, and other key fund characteristics. The industrial
organization literature proposes a variety of models to describe the life cycle evolution of firms.
Empirical evidence shows that industrial firms indeed exhibit distinctive characteristics in terms
of operating performance, strategy, organizational structure, and decision-making style as they
progress through different life cycle stages.8 Mutual funds and industrial firms, as two different
types of corporate organization, share a number of common characteristics. They are both
economic entities engaged in commercial or industrial enterprise with a goal of maximizing the
wealth of owners and shareholders. More importantly, these firms exhibit difficulty in the
reversibility of their life cycle paths due to prior investment in branding and marketing as well as
human capital investment in strategy specific skills. Drawing upon the prior literature, I propose a
mutual fund life cycle model that encompasses stages of incubation, high growth, low growth,
maturity, and decline. A life cycle stage is defined as a time period associated with a common
configuration of variables including asset growth, size, expense ratios, and other pertinent
characteristics. Within this life cycle framework, I study the dynamics in fund performance, net
flows, and other pertinent characteristics. In addition, I investigate the viability of rejuvenation
strategies to reposition a fund to younger life cycle stages, particularly when the fund is in the
stage of decline.
8
Quinn and Cameron (1980) and Miller and Friesen (1984) provide a literature review on various firm life
cycle models. More recently, Diamond (1991), Berger and Udell (1998), and Bulan and Yan (2007) study
the financing behavior of industrial firms over their life cycle. Fama and French (2001), Grullen, Michaely
and Swaminathan (2002), DeAngelo, DeAngelo and Stulz (2005), Bulan, Subramanian, and Tanlu (2007)
find that mature firms are more likely to initiate or increase dividend payout. Anthony and Ramesh (1992)
and Dickinson (2007) show that a firm’s profitability and growth are functions of its life cycle stage. Liu
(2008) provides evidence that accruals decline as a firm becomes mature. There are numerous studies on
bank life cycle including Hunter and Srinivasan (1990), DeYoung and Hasan (1998), Goldberg and White
(1998), DeYoung (1998), and DeYoung, Goldberg, and White (1999).
46
Prior studies have typically addressed the explanation of observed variations in fund
performance from a static perspective. That is, the influence of factors such as age and size is
typically modeled as being constant over a fund’s lifespan. In practice, the interactions between
factors could be dynamic over time as mutual funds correspondingly align their internal attributes
such as investment strategy, fund structure, and managerial characteristics to changes in external
factors such as operating environment, market movements, and technology. Thus, the application
of the life cycle concept to mutual funds could provide an alternative perspective for identifying
potential dynamic relations.
Specifically, I seek to address two main research questions. First, do mutual funds have life
cycle stages associated with different fund characteristics? The industrial organization literature
argues that firms become more mature because of a diminishing investment opportunity set.
Studies of mutual funds such as Chen, Hong, Huang, and Kubik (2002) and Berk and Green
(2004) demonstrate that growth in fund assets will lead to poorer fund performance. Based on
these studies, I argue that a mutual fund’s life cycle evolution is driven by the relative size of its
investment opportunity set, which depends on fund size, managers’ skills, and the investment
opportunities available in the market. Other things being equal, the relative size of the investment
opportunity set decreases when a fund’s total net assets increase. Faced with fewer investment
opportunities, fund managers are likely to experience declining performance, which in turn will
likely lead to decreasing net fund flows. Thus, we expect to observe a declining asset growth as a
mutual fund descends into older life cycle stages.
The second research question investigates whether strategies are available that fund families
can pursue to reposition funds to younger stages in their life cycle. I examine two alternative
strategies, changing the investment objectives or hiring more portfolio managers. These two
strategies could enhance a fund’s capability to identify additional investment opportunities and
therefore improve performance and retain fund growth. This investigation could provide some
insights into how fund families strategically affect a fund’s operation and growth.
47
My sample consists of 2,730 U.S. open-end mutual funds that cover the time period from
January 1961 through December 2005. I construct a composite score measure to classify each
fund’s life cycle stages, using a fund’s age and its one-year and three-year moving average
growth rates. Exploring the explanatory power of alternative life cycle stage measures on the
variations of monthly fund returns, I find that the composite score measure provides information
beyond that contained in fund age.
I perform both univariate and multivariate analysis on fund performance over life cycle
stages. The results indicate that the life cycle effect on fund performance is both economically
and statistically significant, with the magnitude monotonically increasing over life cycle stages.
When a fund develops from the high-growth to low-growth stage, its risk-adjusted monthly
returns drop by 41 basis points. When it reaches the maturity stage, the returns drop by 10 more
basis points. The returns drop again by 29 basis points when the fund descends to the stage of
decline. In addition, net monthly returns and S&P500 excess returns monotonically decrease over
life cycle stages, too. These findings are consistent with the proposed mutual fund life cycle
model in that mutual funds experience poorer performance across stages of their life cycle. I also
find that monthly net fund flows decline monotonically after the high-growth stage. Furthermore,
there are inter-stage differences in total net assets, expense ratios, asset turnover, and the number
of stock held in the portfolio.
My empirical findings shed light on economies of scale in the mutual fund industry. Earlier
studies model the effect of size being constant over a fund’s life cycle and find that an increase in
fund size leads to poorer fund performance. I extend these studies by investigating the scale effect
over a fund’s life cycle stages. The empirical evidence indicates that a marginal increase in size
significantly affects fund performance at the high-growth stage when average fund size is
relatively small. In the case of a $10 million increase in total net assets, the risk-adjusted monthly
returns will drop by 13 basis points. After the fund descends into older stages, however, the
marginal effect of size becomes economically smaller.
48
Finally, I investigate the effectiveness of alternative strategies that fund families have
pursued to rejuvenate fund growth. I compare the one-year stage transition matrices of the funds
that neither changed investment objectives nor hired more portfolio managers with those that
hired more managers and those that changed investment objectives. The stage transition
probabilities show that when a fund is in the decline stage, a change of its investment objective
could rejuvenate fund growth and in the next year reposition the fund to an younger life cycle
stage. Hiring more portfolio managers, however, seems not effective as a way to rejuvenate fund
growth. I also estimate a multinomial logistic regression model of stage transition to further
explore these two strategies. The regression results support the findings of univariate analysis.
Investigating the rejuvenation effect of changing fund’s investment style at different life cycle
stages, my study extends the work by Brown and Goetzman (1993) who find that changing a
fund’s investment style generally lowers performance relative to its peers in the same fund sector.
This paper proceeds as follows. Section 2 proposes a five-stage mutual fund life cycle model.
Section 3 develops the hypotheses. Section 4 addresses the data and reports the descriptive
statistics. Section 5 presents the results of multivariate analysis on the relation between fund
performance and life cycle stages. Section 6 investigates the effectiveness of alternative strategies
that fund families have pursued to rejuvenate fund growth. Section 7 presents the robustness tests
and Section 8 concludes the paper.
2. Mutual fund life cycle model
In this section, I propose a five-stage growth model to describe the life cycle evolution of
mutual funds.
2.1. Incubation stage
Fund families open new funds when the potential to generate additional fee income is
substantial (see, Khorana and Servaes, 1999). According to Arteaga, Ciccotello and Grant (1998),
fund families use two alternative strategies to develop new funds, incubation and selective
49
attention. Under incubation strategy, fund families raise seed money internally to start a number
of small funds and run them in private. After running these seed funds for a while, fund families
will open those funds with good track records to the public but terminate those poorly performing
funds. Under the second approach, fund families launch new funds to the public without an
incubation period whereas devote extra attention to the new funds including subsidizing operating
expenses and more than a proportional allocation of profitable investment opportunities.
Fund families also determine the characteristics associated with a new fund. Massa (1998,
2003) argues that fund families open a series of funds with various styles and fee structures to
exploit investor heterogeneity and increase market share. Nanda, Narayanan, and Warther (2000)
develop a model in which managers set the mutual fund fee structures to maximize the captured
rent, taking into account the effect on fund flows. Bar, Kempf and Ruenzi (2005) show that the
choice of management is a strategic decision made at the fund family level. Fund families also
have power over fund governance. As showed by Tufano and Sevick (1997), fund sponsors select
a new fund’s initial independent board members who accept high fees from the sponsors and in
turn could fail to act in the best interests of fund investors.
2.2. High-growth stage
After opening to the public, new funds generally begin a high-growth phase that is
associated with good performance and large fund inflows. Blake and Timmermann (1998) study
2,300 U.K. open-end mutual funds and find evidence that funds weakly outperform their peers
during their first year after public offerings. Two factors could contribute to the high returns
achieved at the high-growth stage. First, funds at this stage are small. Portfolio managers only
invest in the stocks and industries for which they have informational advantages, which bring
forth high returns (see, Kacperczyk, Sialm, and Zheng, 2005). Second, fund families subsidize
new funds and give them preference in the allocation of resources. For example, Zweig (1996)
and Arteaga, Ciccotello and Grant (1998) both mention that new funds obtain preferential
50
allocations of underpriced IPOs. Gaspar, Massa, and Matos (2006) investigate strategic crossfund subsidization and find that fund families allocate relatively more underpriced IPOs to high
fee, high performance, and young funds. Since young funds have relatively small size, a favorable
allocation of profitable investment opportunities leads to superior performance.
2.3. Low-growth stage
Funds in the low-growth stage are older and larger than those in the high-growth stage. As a
fund’s assets grow, the relative size of the investment opportunity set shrinks. The number of
stocks held by the fund increases as portfolio managers exhaust good investment opportunities for
which they know the best and increase investment in other stocks with which they are less
familiar. As a result, a fund’s returns are relatively lower than those received at its high-growth
stage. Consequently, net flows decrease.
2.4. Maturity stage
The increasing complexity of the investment task from growing assets leads to increasing
transaction costs because of the lessened flexibility that comes with holding larger positions (see,
e.g., Perold and Salomon, 1991; Beckers and Vaughan, 2001; Pollet and Wilson, 2007; Edelen,
Evans, and Kadlec, 2007). As managers continue to invest in those identified good opportunities
(undervalued stocks), large amounts of accumulated purchasing of the same stocks will push
upward prices and thus lower the expected returns. Wermers (2003) find strong evidence that
flow-related additions to existing positions push up stock prices, especially among growthoriented funds. Prior studies also find that the aggregate purchase of the same stock by many
funds will increase the price of the stock. Hong, Kubik and Stein (2005) show that a fund
manager is more likely to buy or sell a particular stock if other managers in the same city are
buying or selling that stock. Wermers (1999) find empirical evidence that mutual fund herding
speeds up the incorporation of new information in stock prices.
51
A manager’s incentive to retain and attract assets under management contributes to poorer
fund performance over life cycle stages of the fund. Jensen’s (1986) free cash flow theory
suggests that managers of industrial firms with large free cash flows are more likely to diversify
in value-destroying projects after they exhaust all investment opportunities. This is analogous to
the mutual fund industry. Because the management fee is a percentage of the total assets under
management, managers have a propensity for over-investment and begin to adopt passive
investment strategies when they have exhausted all lucrative investment opportunities with a
large amount of “free” money at hand. Chen, Hong, Huang, and Kubik (2002) and Berk and
Green (2004) argue that managers invest a larger portion of fund assets in benchmark portfolios
as funds grow. Chen et al. (2002) further argue that the rationale behind this behavior is that
managers no longer care about maximizing fund returns after funds reach a certain size. A
potential explanation for managers’ losing interest in maximizing returns is that managers realize
that they are unable to find more profitable investment opportunities.
Funds obtain lower average returns in the maturity stage than in the low-growth stage
because of larger trading costs, declining-profit opportunities, and overinvestment. As a result,
the average fund inflows are lower than they were in the growth stages but fund outflows are
higher. Some funds chose to close to avoid these scale diseconomies. Nevertheless, earlier studies
find that closing a fund does not protect its performance in the next period (see, Zhao, 2004; Bris,
Gulen, Kadiyala, and Rau, 2007). One possible explanation for their findings is that fund size is
already too large when the fund was closed.
2.5. Decline stage
Because of large trading costs, absence of profitable opportunities, and severe
overinvestment, mutual funds at the stage of decline experience extremely poor performance and
52
large cash outflows. Fund families have incentives to create and market “star” funds but eliminate
poorly performing funds, and thus they are likely to terminate small funds with declining returns.9
2.6. A general descending life cycle path
Industrial firms can not readily reverse the evolution process without incurring significant
costs. The reason for this difficulty in reversibility is that many expenditures and investments are
at least partly irreversible. For example, the expenditure in marketing a particular product is
irreversible. The firm will lose the brand value of the old product if it totally changes its product
line. A project can be firm specific and therefore it can not be sold to a different firm at a price
that fully covers investment. Furthermore, executives’ experience and skill is often restricted to
some specific areas. A firm could lose the value of investment in human capital if it changes its
operating strategy. Thus, once some expenditure or investment is made, a firm either cannot
return to the previous state immediately or would incur some costs in doing so (see, Baldwin,
1982; Pindyck, 1988, 1991).
Like the counterpart of an industrial firm, a mutual fund’s life cycle evolution path is also
not readily reversible because of the investments in marketing and human capital. As the relative
investment opportunity set shrinks over a fund’s life cycle stages, it becomes harder for fund
managers to find profitable opportunities to support continued growth. Although managers could
identify additional investment opportunities through some strategies such as changing their
investment strategies or objectives, such changes are constrained by a fund’s prospectus and a
change in investment objective requires the approval of the majority of fund holders. 10
9
For a discussion of mutual fund exit strategy such as merger and liquidation, see Jayaraman, Khorana, and
Nelling (2002), Zhao (2005), and Ding (2006).
10
The Investment Company Act of 1940 Section 13(a) states “No registered investment company shall,
unless authorized by the vote of a majority of its outstanding voting securities…deviate from its policy in
respect of concentration of investments in any particular industry or group of industries as recited in its
registration statement, deviate from any investment policy which is changeable only if authorized by
shareholder vote, or deviate from any policy recited in its registration statement pursuant to section
8(b)(3)…”
53
Furthermore, changing a fund’s investment objective will entail other significant costs. First, a
fund has invested in marketing and advertising with respect to the declared objective. If the fund
changes its investment objective, its brand value associated with the old objective will vanish.
Second, a portfolio manager’s experience and skill could be strategy or style specific. His
expertise may not be readily transferable if the fund changes its investment objective. Therefore,
mutual funds evolve into their older life cycle stages in a general descending manner, and they
would incur significant costs to return to younger stages.
3.
Hypothesis Development
Funds in early stages of their life cycle are usually small. Managers do not have enough
money to fully exploit all of the good investment opportunities they can identify, and thus invest
in the best investment opportunities with the highest expected returns. Therefore, mutual funds
achieve supreme performance in their early stages. As funds grow up, managers exhaust their best
investment opportunities and thus have to invest in the second-best and thereafter declining-profit
opportunities. The average return decreases accordingly, and the growth rate declines. Eventually,
managers have exhausted all investment opportunities. As a result, performance is poor leading to
net fund outflows. In the stage of decline, managers have to overinvest and adopt a passive
investment strategy, which gives rise to much lower returns followed by larger amount of net
cash outflows. Based on this reasoning, I posit that older life cycle stages are associated with
poorer fund performance.
Prior studies such as Chen et al. (2002) find that an increase in size leads to lower fund
performance. These studies model the marginal effect of size as being constant over a fund’s life
cycle. However, this assumption could be skeptical because funds vary in size over their life
cycle and thus the same amount of increase in assets on a larger base should have a smaller effect
on performance. The mutual fund life cycle model predicts that fund size is relatively small in the
54
high-growth stage, but larger in older stages. Therefore, I expect that the marginal effect of size is
stronger in the high-growth stage, but weaker in older stages.
When a fund reaches older stages in its life cycle, performance becomes poorer and asset
growth declines. Fund families have high incentives to reboot fund growth because the
management and advisor fee is a percentage of the assets under management. Canals (2001)
argues that “… managers should look at corporate growth from a dual perspective: the internal
dimension of resources and capabilities and the external dimension of markets and customers.”
To obtain growth from the external dimension of markets and customers, fund families seek to
attract more fund inflows by pursuing strategies such as increasing advertising, reducing fees, and
creating multiple share classes. Prior studies such as Sirri and Tufano (1996), Jain and Wu (2000),
and Barber, Odean, and Zheng (2005) find that increasing marketing expenses can attract more
fund inflows. Christoffersen (2001) find evidence that poorly performing funds waive fees to
adjust net returns to investors. As described in Nanda, Wang, and Zheng (2005), mutual funds
tend to create multiple share classes to attract more investors with different preferences for fee
structure.
This paper focuses on the internal dimension of growth: resources and capabilities. Fund
families can pursue some strategies to increase the fund’s resources and also enhance its
capabilities to identify additional investment opportunities. One potential strategy is to hire more
portfolio managers, a step that could help generate more investment ideas. Another potential
strategy is to change the investment objective. By changing a fund’s investment objective,
managers could have an expanded investment opportunity set and more flexibility in choosing
stocks. I hypothesize that these two strategies can improve fund performance and thus reposition
funds to their younger life cycle stages.
55
4.
Data description
4.1. Data sources
Several sources are employed to create the main data set by merging the survivorship-biasfree mutual fund database from the Center for Research in Security Prices (CRSP) with the
Thomson Financial mutual fund holding database and the CRSP stock database. The CRSP
mutual fund database includes information on mutual fund monthly returns, total net assets
(TNA), inception dates, fee structure, fund investment objectives, asset turnover ratios, managers’
names (begins 1992), management company names (begins 1993), and other fund characteristics.
The Thomson Financial mutual fund database provides quarterly or semiannual reported
stockholdings of U.S. mutual funds. I merge these two databases using MFLINKS from Wharton
Research Data Services (WRDS). I link each stock in the portfolios to the CRSP stock database to
find its industry classification code (SIC). Less than 0.67% of all holding-stock observations lack
a SIC code. The number of distinct four-digit SIC code in a given portfolio is used as a proxy for
industry concentration. Because one fund could have multiple share classes, I compute the total
net assets of a fund as the summation of the total net assets in each share class. Weighting each
share class by its total net assets, I obtain the value-weighted averages of monthly net returns,
expense ratios, asset turnover ratios, and fee structures at the fund level.
To be included in the sample, several criteria are employed. First, each fund in the sample
must have operated for at least three years. 11 Second, I eliminate the balanced, bond, index,
international, and sector funds because I focus on actively managed equity funds that invest
mainly in the U.S. stock market. I used the Wiesenberger (WI) fund type code, the ICDI fund
objective code, and Standard & Poor’s detailed objective code to categorize funds as Growth fund,
Growth and Income fund, and Income fund, as described in Appendix A. My final sample of
11
Funds with a history that is shorter than three years are less likely to experience distinctive life cycle
stages.
56
2,730 mutual funds covers the period from January 1961 to December 2005, and fund holding
data covers the period from January 1980 to December 2005.
In addition to reported monthly returns, I examine S&P500 excess returns and abnormal
returns adjusted by Carhart’s (1997) four factors. I employ time series regression with Carhart
(1997) four-factor model to calculate loadings on different risk factors, using lagged 24 monthly
returns. Using these risk loadings, I obtain risk-adjusted returns for the next period. I construct
several control variables. LogTNA is the natural logarithm of one plus total net assets. LogFamily
is the natural logarithm of one plus the size of the family the fund belongs to. Age is the number
of years since the inception of the mutual fund. Total load is the total front-end, deferred, and
rear-end load charged by the fund. Flows are monthly net fund flows into the mutual fund divided
by its total net assets. It equals [TNAt − TNAt −1 ⋅ (1 + rt )] / TNAt , where rt is the net return at
month t. Industry Number is the number of the distinct four-digit SIC code in the portfolio. Stock
Number is the number of all domestic stocks in the portfolio. Manager Number captures the
number of portfolio managers running the fund. For those funds listed as “team,” “committee,” or
“multiple,” I follow Chen et al. (2002) and set the manager number to four. Thus, Manager
Number takes on a value of one, two, three, or four.
4.2. Life cycle stage measure
Using a good instrument for a mutual fund’s life cycle is critical in empirical research. Prior
studies usually treat fund age as a proxy for a fund’s life cycle. The validity of age as a good life
cycle proxy, however, is questionable. According to Churchill and Lewis (1983), the age of an
organization alone is unlikely to provide a valid reflection of its life cycle stages. Using age to
proxy a fund’s life cycle implicitly assumes that all funds have the same speed of development,
which is unreasonable. For example, at age 10, Fund A reaches $100 million in size and
experiences low returns and thus low growth because its manager has exhausted all investment
57
opportunities. In contrast, at age 10, Fund B reaches $100 million and still achieves high returns
and thus high growth because its manager is more skilled than Fund A’s manager in finding good
investment opportunities. Obviously, the two funds of the same age have different relative size of
opportunity set and accordingly locate in different stages of their life cycle. Therefore, using age
as a life cycle proxy can mix the information provided by funds that locate in different stages.
Another disadvantage of using age is that it is hard to determine which age corresponds to which
life cycle stage without additional information provided by other variables. Similarly, two funds
of the same size can be in different life cycle stages if they have different relative size of
investment opportunity set. Therefore, size per se fails as a good life cycle proxy, too.
I construct a composite score measure to classify a fund’s life cycle stages, using fund age
and its one-year and three-year moving average growth rates. The mutual fund life cycle model
predicts that a fund experiences decreasing asset growth over stages of its life cycle, and therefore
a fund’s growth rate includes some information on the relative size of the investment opportunity
set and corresponding life cycle stages. I adjust a fund’s annual growth rate by annual market
return to exclude the influence of market movement on fund value, and use the three-year moving
average growth rate to smooth the evolution process.12 Then, I rank all fund-year observations in
ascending order into four quartiles based on age, growth, and moving average growth,
respectively.
Next, I match each fund-year observation in terms of the three variables mentioned above to
the cells in the table illustrated in Appendix B. Any matching cell will gain one point and other
cells gain zero. I sum all points within the same stage column to obtain a composite score for
each stage. The stage column that scores highest will assign the corresponding life cycle stage to
the given fund year. In a case in which three stages have the same highest score, I choose the
stage in the middle. I do not empirically study the incubation stage because of the lack of data.
12
Provided by CRSP, this market return is a value-weighted return of a portfolio of all stocks in the NYSE,
Amex, and Nasdaq. Adjusting annual growth rate by the mean return of all funds in the same fund sector
produces very close results.
58
4.3. Descriptive statistics
After using the composite-score measure to classify a fund’s life cycle stages for all fundyears, for each fund age I calculate the percentage of funds located in the life cycle stages of
high-growth, low-growth, maturity, and decline, respectively. As a result, I obtain four age-series
of fund percentage as demonstrated in Fig. 1. The graph shows that, in general, funds locate in the
high-growth stage when they are young and progress to older life cycle stages as they age.
However, old funds do not all stay at the stage of maturity or decline. For funds that are 30 years
old, about 3% locate in the high-growth stage, 12% in the low-growth stage, 36% in the maturity
stage, and only 49% in the stage of decline. These findings suggest that age is not a good proxy
for life cycle stages.
I also explore the stage transition matrices presented in Table 1 to gain more insight into the
process of mutual fund life cycle evolution. P1, P4, and P9, respectively, indicate the stage
transition matrices in the second, fifth, and tenth year. For funds that locate in the high-growth
stage, 37% remain in the same stage in the next year, 41% drop to the low-growth stage, 16%
descend to the maturity stage, and only 6% devolve to the decline stage. After four years, only
17% of the funds remain in the high-growth stage, 36% fall to the low-growth stage, 31% reach
the maturity stage, and 15% devolve to the stage of decline. After nine years, only 7% of the
funds remain in the high-growth stage, 22% descend to the low-growth stage, 38% devolve to the
maturity stage, and 32% drop to the decline stage. These stage transition patterns indicate that
funds progress smoothly from young to older life cycle stages, which is consistent with the
findings in Fig. 1.
Table 1 also indicates that declining funds do not necessarily stay forever in the decline stage.
Some of the declining funds rejuvenated and repositioned to younger life cycle stages. The
percentage of declining funds that remain in the decline stage after one year is 68%. This number
59
drops to 52% after four years and 41% after nine years. This evidence suggests that, like
industrial firms, declining funds can revive.
Table 2 presents the descriptive statistics of sample funds in each life cycle stage. All
variables are winsorized at one and the 99th percentile.13 I observe that the distributions of some
variables are highly skewed. For example, the mean of TNA in the high-growth stage is $283
million, but the median is only $71 million. In other stages the means of TNA are much higher
than the medians, too. Therefore, I focus on medians in the following analysis. Net monthly
returns, S&P500 excess returns, and four-factor adjusted returns are all monotonically decreasing
over life cycle stages, as demonstrated in Fig. 2. The median test shows that performance shifts
between stages are statistically significant at the 1% level. Chevalier and Ellison (1997) and Bar,
Kempf, and Ruenzi (2005) find that young funds are more likely than old funds to take high risk.
Managers of young funds may invest in stocks with high systematic risk, which could result in
the observed higher total return in earlier life cycle stages. The risk-taking behavior of fund
managers, however, cannot explain the monotonically decreasing four-factor adjusted returns.
The decreasing risk-adjusted return over stages is much more consistent with the hypothesis that
funds progress through their life cycle paths with a diminishing investment opportunity set.
Table 2 also indicates that mutual funds charge different expenses ratios in different life
cycle stages. The median expense ratios vary from 1.37% in the high-growth stage to 1.22 % in
the low-growth stage, 1.17% in the maturity stage, and 1.28% in the stage of decline. The median
test shows that the changes in expense ratios between stages are statistically significant. This
finding is consistent with prior studies in that expense ratios decrease with fund size (see,
Malhotra and McLeod, 1997; Lazko, 1999; Rea, Reid, and Millar, 1999; LaPlante, 2001; Warner
and Wu, 2006).14
13
The multivariate analyses produce very similar results when variables are winsorized at 5 and the 95th
percentile.
14
Dermine and Roller (1992) study 137 French mutual funds and find that expense ratio decreases and then
increases as fund size becomes larger.
60
The annual asset turnover ratios decrease over the high-growth, low-growth and maturity
stages. This pattern implies that larger fund size leads to less flexibility in changing holding
positions, and hence managers have less incentive to trade. However, in the decline stage the
asset turnover jumps to 0.77, which is higher than in the high-growth stage. Given the fact that
fund size in the decline stage is larger than it is in the high-growth stage, the higher turnover ratio
in the decline stage suggests that managers trade more frequently than they do in other stages.
Another reason for this high asset turnover could be that managers have to sell their holdings
because of a large amount of redemption. Fig. 3 shows the dynamics of turnover ratios over life
cycle stages.
Fig. 4 illustrates another finding from Table 2 that monthly net fund flows monotonically
decrease over life cycle stages. In the low-growth stage, funds achieve positive S&P500 access
returns but negative four-factor adjusted returns. However, investors respond with positive net
fund flows. This evidence suggests that some fund investors do not use risk-adjusted returns to
evaluate fund performance, which is consistent with the findings in Gruber (1996), Sirri and
Tufano (1998), and Del Guercio and Tkac (2002).
I also observe from Table 2 that the number of stocks and the number of industry in portfolio
shift between life cycle stages. Median tests show that almost all of these shifts are statistically
significant. Both stock number and industry number increase from the high-growth to low-growth
stage but decrease after the maturity stage although the size at the maturity stage is larger than
that at the low-growth stage. This finding is not inconsistent with the hypothesis that managers
are constrained by the size of the fund, other things being equal. My explanation is that the
investment opportunity set is dynamic. For example, when a fund is at the low growth stage the
identified investment opportunities locate in 50 stocks. As time goes by, fund size increases.
Nevertheless, the manager focuses his investments in only 40 stocks because the market changed
and thus he can not find more good investment opportunities. So, the number of stock in portfolio
could drop even if fund size increases.
61
Table 3 presents correlations between main variables.
4.4. Life cycle effect vs. scale effect
Although Table 2 indicates that average fund size increases from the high-growth to maturity
stage and that size in the decline stage is much larger than in the high-growth stage, it is
premature to conclude that the increasing scale of size is the only reason for the decreasing
performance over stages observed in Fig. 2. In the mutual fund life cycle model, the declining
performance over stages is driven by the decreasing relative size of the investment opportunity set,
which depends on fund size, managerial skills, and the opportunities available in the market. The
increasing scale cannot fully explain the life cycle effect on performance.
To distinguish scale effect from life cycle effect, I conduct the following data mining.
Within each life cycle stage, I rank fund-month observations by size into quartiles, with the fourth
quartile having the largest size. Next, I choose the fourth quartile in the high-growth stage, the
third quartile in the low-growth stage, and the second quartile in both the maturity and decline
stages so that the average size of the sample funds decreases over stages. Finally I calculate the
medians and means of monthly returns of these chosen quartiles and report the results in Table 4.
I observe that all three measures of fund performance monotonically decrease over the
chosen quartiles. Because average fund size of the chosen quartiles monotonically declines, the
scale effect is not responsible for the poorer performance over life cycle stages. This finding
suggests that, in addition to scale, there are other factors that lead to declining performance over
stages.
5.
Mutual fund performance and life cycle stages
5.1. Regression of four-factor adjusted returns
I estimate pooled OLS, random effect, and fixed effect panel regression models to further
investigate the relation between fund performance and life cycle stages. I regress monthly four-
62
factor adjusted returns on dummies of life cycle stages, fund size, the interactions of stage
dummies with fund size, and other fund characteristics. The variables of life cycle stage are
lagged for one year while other independent variables are lagged for one month. Following
Petersen (2007), I correct for the fund effect and the time effect in the pooled OLS regression.
The regression specification is
4
Ri,t = α + ∑ Dk LifeCyclei,t −1, k + β1 LogTNAi,t −1
k =2
4
+ ∑δ k LogTNAi,t −1 × LifeCyclei,t −1, k +γΧi,t −1 + ε i ,t ,
(1)
k =2
where R is the four-factor adjusted return; LogTNA is the natural logarithm of one plus TNA;
LifeCyclek consists of three dummy variables that indicate the low-growth, maturity, and
decline stages; X is a set of control variables that includes asset turnover, expense ratios, total
loads, fund flows, and dummies of fund sectors. Table 5 presents the regression results.
In Model 1, the coefficients of LowGrowth, Maturity, and Decline are -40.64, -51.31, and 80.37, respectively. The Wald test shows that these coefficients are statistically different from
each other at the 1% level. These findings indicate that the life cycle effect on fund performance
is monotonically increasing across stages. The observed increasing life cycle effect is consistent
with my mutual fund life cycle model in that when a fund develops over life cycle stages, the
relative size of the investment opportunity set shrinks and thus performance declines. Since I
include fund size in the regression specification, the observed life cycle effect is not likely driven
by the scale. The random effect and fixed effect regression models produce consistent results.
Next, I examine the interactions between fund size and life cycle stages. The results of OLS
regression indicate that, in the high-growth stage (as the reference group), fund size has a
negative effect on performance and is statistically significant at the 1% level. For a $10 million
63
increase in size, the four-factor adjusted monthly return will decrease by about 13 basis points.15
Wald test cannot rejects the null that the sum of the coefficient of LogTNA and the coefficient of
LogTNA*LowGrowth equals zero, or the null that the sum of the coefficient of LogTNA and the
coefficient of LogTNA*Maturity equals zero. On the other hand, Wald test reject the null that the
sum of the coefficient of LogTNA and the coefficient of LogTNA*Decline equals zero. However,
I can not conclude that the size effect is positive at the stage of decline because of the inconsistent
statistics in both random effect and fixed effect models. For random effect specification, Wald
test reject the null that the sum of the coefficient of LogTNA and the coefficient of
LogTNA*LowGrowth equals zero and the null that the sum of the coefficient of LogTNA and the
coefficient of LogTNA*Maturity equals zero. However, the test cannot reject the null that the
sum of the coefficient of LogTNA and the coefficient of LogTNA*Decline equals zero，which
suggests that future performance is not related to fund size at the decline stage. Since declining
funds experience negative net fund flows, this evidence is consistent with the finding in Bris et al.
(2007) that there is not a negative relation between size and four-factor α when funds experience
low net fund flows. The results of the fixed effect panel regression imply a decaying scale effect
across the four stages. Overall, I find solid evidence that the marginal effect of size is larger in the
high-growth than in older life cycle stages.
5.2. Composite score measure vs. age measure
In this section I investigate whether my composite score measure is better than fund age to
proxy for mutual fund life cycle. I construct another life cycle measure using age alone. I rank all
fund-year observations by age in ascending order into four quartiles, with the first quartile having
the youngest age. Fund years at the first quartile are assigned to the high-growth stage, while
those at the fourth quartile are assigned to the decline stage. Table 6 presents the results of
15
The marginal effect = (-5.404) x Log(1+10) = -13.
64
regression of monthly returns on life cycle stages classified with alternative life cycle stage
measures.
In Model 1 where the composite-score measure is used, the coefficients of fund size, life
cycle stages and interactions between size and life cycle stages are all statistically significant at
the 1% level. In Model 2 where the age measure is used, the coefficient of LogTNA and the
coefficient of LogTNA*LowGrowth is not even statistically significant at the 10% level. To
further explore whether the composite-score measure provides information beyond that contained
in the age measure, I conduct the following J-test procedure for testing between the two nonnested regression models.16
First, I estimate Model 1 and Model 2 in Table 6 and calculate the sets of fitted values for
the dependent variable. Then I estimate a regression specification based on Model 1, but also
using the fitted value obtained from Model 2 as an added explanatory variable. I also estimate a
regression specification based on Model 2 using the fitted value from Model 1 as an added
explanatory variable. The null hypothesis is that the composite score measure provides more
information than the age measure and Model 1 fits the data better. The null hypothesis is
supported if the estimate of the coefficient of the fitted value from Model 1 is significantly
different from zero and the estimate of the coefficient of the fitted value from Model 2 is not
significant. If both estimates are significantly different from zero, then each measure provides
some information not present in the other and the null is rejected. If both estimates are
insignificant, then both measures provide similar information and neither measure is superior to
the other. Table 7 presents the J-test results.
For the regression based on Model 2, the coefficient of the fitted value from Model 1 is
1.128 and different from zero at the 1% significance level. For the regression based on Model 1,
the coefficient of the fitted value from Model 2 is not statistically different from zero. These
16
For a discussion of the J-test procedure, see Davidson and MacKinnon (1981) and McAleer (1995).
65
results suggest that the composite score measure provides information beyond that contained by
the age measure.
6.
Rejuvenation strategy
In this section, I investigate the effects on life cycle evolution of changing fund investment
objectives or hiring more portfolio managers. The sample used includes 2,229 funds covering the
time period from 1993 through 2005. In this sample, 908 funds neither changed their investment
objectives nor hired more managers within the time period. Among the 287 events of changing
objectives, I use 268 events that have second-year observations. There are 1,462 incidents of
adding managers from which I use 1,357 events that have second-year observations.
6.1. Stage transition matrices
I compare the one-year stage transition matrices of funds that neither changed their
investment objectives nor hired more portfolio managers (as a reference group) with those that
hired more portfolio managers and those that changed the investment objectives. If these two
rejuvenation strategies work, compared with the reference group, funds that changed their
investment objectives or hired more managers should in the next year have higher transition
probabilities to younger life cycle stages.
Table 8 presents next-year stage transition matrices of funds that neither hired more
managers nor changed fund objectives (no-strategy funds in Panel A), those of funds that changed
the investment objectives (in Panel B), and those of funds that hired more portfolio managers (in
Panel C). Comparing Panel A and Panel B, I find that when funds are in the low-growth stage
changing their investment objectives has no effect on the probabilities of transition to younger life
cycle stages. When funds are in the maturity stage, however, changing their investment objectives
seems to decrease the probability of descending to older life cycle stages. As observed, 12% of
the funds in Panel B devolve to older stages in the next year vs. 20% in Panel A. When funds are
66
in the decline stage, changing the investment objectives seems to increase the probability of
developing to younger life cycle stages. In the decline stage, totally 33% of the funds in Panel B
evolve to younger stages in the next year vs. only 17% in Panel A.
The strategy of hiring more portfolio managers seems not effective in rejuvenating fund
growth, as I observe no significant difference in the rejuvenation probabilities between Panel A
and Panel C. For funds in the low-growth stage, the rejuvenation probability to the high-growth
stage in the next year is 5% in both Panel A and Panel B. For funds in the maturity stage, 10% in
Panel C reposition themselves to younger stages in the next year vs. 9% in Panel A. For funds in
the stage of decline, 18% in Panel C develop to younger stages in the next year vs. 17% in Panel
A.
6.2. Multinomial logistic regressions
I estimate a multinomial logistic regression model to further investigate the effectiveness of
the two strategies. The dependent variable has a category value of 0, 1, and 2, respectively, which
indicates transition in the next year to the same, younger, or older life cycle stages. The
regression specification is
4
yi ,t = α + ∑ Dk LifeCyclei ,t −1, k
k =2
4
+ β1Obji ,t −1 + ∑ β k Obji ,t −1 × LifeCyclei ,t −1, k
k =2
(2)
3
+ δ 1 Mgri ,t −1 + ∑ δ k Mgri ,t −1 × LifeCyclei ,t −1, k +γΧ i ,t −1 + ε i ,t ,
k =2
where LifeCycle k consist of stage dummies for the low-growth, mature and decline stages; Obj is
the dummy variable for changing the investment objectives; Mgr is the dummy variable for hiring
more managers; X is a set of control variables that includes fund size, expense ratios, total load,
asset turnover ratios, and dummies of fund sectors. In this regression model, the reference group
67
consists of the high-growth funds that neither changed investment objectives nor hired more
portfolio managers.17 Table 9 presents the regression results.
Because life cycle stage dummies interact with strategy dummies in the regression model, I
am able to find the marginal effect of each strategy in every life cycle stage.18 I do not study the
strategies in high-growth stage because funds can not rejuvenate from high-growth to incubation
stage. In Model 1, the coefficient of Objective*LowGrowth and that of Objective*Maturity are
not statistically significant, which indicates that changing investment objectives will not
rejuvenate fund growth when the fund is at the low-growth or maturity stage. The coefficient of
Objective*Decline is 0.870 and statistically significant at the 1% level. This indicates that
compared with no-strategy declining funds declining funds that change investment objectives are
likelier to rejuvenate than remain in the decline stage. Hiring more portfolio managers seems to
carry no rejuvenation effect because two of the coefficients of the interactions between the
dummy for adding manager and dummies for life cycle stages are not statistically significant and
the third one is negative.
Overall, hiring more portfolio managers appears to have no rejuvenation effect. This finding
complements prior studies which show that team-managed funds perform no differently (Bliss,
Potter, and Schwarz, 2006) or worse (Chen, Hong, Huang, and Kubik, 2002; Bar, Kempf, and
Ruenzi, 2005; Massa, Reuter, and Zitzewitz, 2007). In contrast, there is a strong rejuvenation
effect from the strategy of changing investment objectives when a fund locates in the stage of
decline.
17
In an alternative regression model, the interaction of Manager*Decline is included but its standard errors
and t-statistics are not reported in the output. I consulted with the software provider, StataCorp. They said
that regression results with missing standard errors and t-statistics are skeptical.
18
I include Objective*Manager and its interaction with stage dummies in another regression model.
However, these terms are dropped automatically due to a collinearity problem.
68
7.
Robustness
7.1. Regression of three-month cumulative returns
To exclude the possibility that the results of the regression of monthly returns are driven by
the frequency of the monthly data, I estimate the regression model (1) using three-month
cumulative four-factor adjusted returns as the dependent variable and reports regression results in
Table 10.
The results show that the life-cycle effect on performance is both economically and
statistically significant, with the negative effect monotonically increasing from the low-growth to
decline stage. In Model 1, the coefficient of LowGrowth is –122; the coefficient of Maturity is –
145; the coefficient of Decline is -225. I perform a Wald test and find that these coefficients are
statistically different at the 1% level. The results of random effect and fixed effect regressions are
consistent. The differences in the coefficients of interaction between size and stage dummies
indicate a decreasing negative effect of size on performance over stages. Overall, the results of
the regression of three-month cumulative returns have similar implications to those of the
regression of monthly returns.
7.2. Alternative life cycle measure
Using growth rate, three-year average growth rate, and fund age, I construct a composite
rank as another measure to classify a fund’s life cycle stages. Based on the method used by Liu
(2008), I rank all fund years into percentile with respect to the market-adjusted growth rate so that
funds in the lowest percentile have the highest growth rates. I also rank the three-year average
growth using the same procedure. Next, I rank fund-years based on fund age in ascending order.
And then I calculate a composite rank as the average of the three percentile rankings. Fund-years
with a composite rank of less than 25% will be assigned to the high-growth stage, those between
25% and 50% are assigned to the low-growth stage, those between 50% and 75% to the mature
stage, and those of more than 75% to the stage of decline. After classifying life cycle stages using
69
the composite rank measure, I perform both univariate and multivariate analysis and obtain
consistent results.
7.3. Time sensitivity tests
I estimate the regression model (1) using observations after 1980, 1990, and 2000,
respectively. The results of these regressions have similar implications to those of the regression
using the whole data set. These time sensitivity tests suggest that my finding of life cycle effect
on performance is not driven by the data from a specific time period.
7.4. Life cycle evolution of long-life funds
Mutual funds with a short history could experience a different “aging” process from that of
funds that have (had) existed for a long time. Including funds that died young in the sample is
likely to bias downward the performance of young funds at early stage and/or bias upward the
transition probabilities to older life cycle stages as time goes by. To obtain more insights into the
life cycle path of long-life funds, I redo all analyses with a subset sample which consists of 1,349
funds that have (had) operated for at least 10 years.
The results indicate that the median (mean) risk-adjusted monthly return at the high growth
stage is 0.0008 (0.0017), which is larger than the number 0.0002 (0.0013) obtained using the
whole sample. Furthermore, the stage transition matrices imply that the “aging” process of a longlife fund is slower than that of an average fund. For a long-life fund located at the high growth
stage, the probability of remaining at the same stage is 0.71 after one year, 0.30 after four years,
and 0.14 after nine years. However, using the whole sample including funds that died young tilts
these numbers downward to 0.37, 0.17, and 0.07 as reported in Table 1. All other results are close
to those of main analyses.
70
8. Conclusion
I propose a mutual fund life cycle model that encompasses stages of incubation, high growth,
low growth, maturity, and decline. This model provides an alternative dynamic perspective with
which we can study various issues in the mutual fund industry such as fund performance,
performance persistence, managerial behaviors, and fund family strategies. I examine a sample of
2,730 U.S. open-end mutual funds and find strong empirical evidence that is consistent with the
mutual fund life cycle model.
There are inter-stage differences in fund size, expense ratios, and number of stock held in the
portfolio. Asset turnover decreases over the high-growth, low-growth, and maturity stages, but
increases abnormally at the stage of decline. Net fund flows monotonically decrease over life
cycle stages. Furthermore, net returns, S&P500 excess returns, and risk-adjusted returns all
monotonically decrease after the high-growth stage. I explore further and verify that the scale
effect is not the only force that drives the poorer performance across life cycle stages. I also find
that the marginal effect of size is strongest in the high-growth stage but weaker in older life cycle
stages.
Finally, I investigate the effectiveness of alternative strategies pursued by fund families to
rejuvenate fund growth. The empirical evidence indicates that, when a fund is in the decline stage,
changing its investment objective will increase the probabilities of transition to younger life cycle
stages in the next year. There is no evidence, however, that the strategy of hiring more portfolio
managers is effective in rejuvenating fund growth.
71
Appendix A
Mutual fund investment objective categorization
This appendix lists the Wiesenberger (WI) fund type code, the ICDI fund objective code, and Standard &
Poor’s (S&P) objective code provided in the CRSP mutual fund database that are used to categorize funds
as Growth fund, Growth and Income fund, and Income fund. The Wiesenberger fund type code is available
through 1993. The ICDI fund objective code is available from 1993 through July 2003. Standard &Poor’s
detailed objective code begins in 1993.
Fund Style
Investment Objective Code
Growth Fund
WI: SCG AGG G LTG MCG G-S S-G GRO
ICDI: AG AGG LG
S&P: SCG AGG GRO
Growth and Income Fund
WI: GCI G-I G-I-S G-S-I I-G I-G-S I-S-G S-G-I S-I-G GR
ICDI: GI TR
S&P: GRI ING GMC
Income Fund
WI: I I-S IEQ ING
ICDI: IN
S&P: ING
72
Appendix B
Mutual fund life cycle stage scoring table
This appendix describes the scoring table used to classify mutual fund life cycle stages. I rank all fund-year
observations in ascending order into four quartiles based on fund age, annual asset growth rate, and 3-year
moving average growth, respectively. Next, I match each fund-year observation in terms of the three
variables to the cells in the table. Any matching cell will gain one point and other cells gain zero. I sum all
points within the same stage column to obtain a composite score for each stage. The stage column that
scores highest will assign the corresponding life cycle stage to the given fund year. In a case in which three
stages have the same highest score, the stage in the middle is chosen.
Variable
High Growth
Low Growth
Maturity
Decline
Age
quartile 1
quartile 2
quartile 3
quartile 4
Growth
quartile 4
quartile 3
quartile 2
quartile 1
3-Year
Growth Moving Average
quartile 4
quartile 3
quartile 2
quartile 1
Stage Score
73
References
Anthony, J.H., Ramesh, K., 1992. Association between accounting performance measures and
stock prices. Journal of Accounting and Finance 15, 203-227.
Arteaga, K.R., Ciccotello, C.S., Terry Grant, C.T., 1998. New equity funds: marketing and
performance. Financial Analyst Journal 54, 43-49.
Baldwin, C.Y., 1982. Optimal sequential investment when capital is not readily reversible.
Journal of Finance 37, 763-782.
Bar, M., Kempf, A., Ruenzi, S., 2005. Team management and mutual funds. working paper,
University of Cologne, Germany.
Barber, B.M., Odean, T., Zheng, L., 2005. Out of sight, out of mind: the effects of expenses on
mutual fund flows. Journal of Business 78, 2095-2119.
Beckers, S., Vaughan, G., 2001. Small is beautiful. Journal of Portfolio Management 27, 9-17.
Berger, A.N., Udell, G.F., 1998. The economics of small business finance: the roles of private
equity and debt markets in the financial growth cycle. Journal of Banking and Finance 22, 613673.
Berk, J.B., Green R.C., 2004. Mutual fund flows and performance in rational markets. Journal of
Political Economy 112, 1269-1295.
Blake, D., Timmermann, A., 1998. Mutual fund performance: Evidence from the UK. European
Finance Review 2, 57-77.
Bliss, R., Potter, M., Schwarz, C., 2006. Performance characteristics of individual vs. team
managed mutual funds. working paper, Babson College and University of Massachusetts.
Bris, A., Gulen, H., Kadiyala, P., Rau R., 2007. Good stewards, cheap talkers, or family men?
The impact of mutual fund closures on fund managers, flows, fees, and performance. Review of
Financial Studies 20, 953-982.
Brown, S.J., Goetzmann, W.N., 1997. Mutual fund style. Journal of Financial Economics 43,
373-399.
Bulan, L., Yan, Z., 2007. The pecking order of financing in the firm’s life cycle. working paper,
Brandeis University and Millennium Partners LLP.
Bulan, L., Subramanian, N., Tanlu, L., 2007. On the timing of dividend initiations. Financial
Management, forthcoming.
Canals, J., 2001. How to think about corporate growth? European Management Journal 19, 587598.
Carhart, M.M., 1997. On persistence in mutual fund performance. Journal of Finance 52, 57-82.
74
Chen, J., Hong, H., Huang M., Kubik, J.D., 2002. Does fund size erode mutual fund performance?
The role of liquidity and organization. American Economic Review 94, 1276-1302.
Chevalier, J., Ellison, G., 1997. Risk taking by mutual funds as a response to incentives. Journal
of Political Economy 105, 1167-2000.
Christoffersen, S.E.K., 2001. Why do money fund managers voluntarily waive their fees? Journal
of Finance 56, 1117-1140.
Churchill, N.C., Lewis, V.L., 1983. The five stages of small business growth. Harvard Business
Review 61, 30-35.
Davidson, R., MacKinon, J.G., 1981. Several tests for model specification in the presence of
alternative hypotheses. Econometrica 49, 781-793.
DeAngelo, H., DeAngelo, L., Stulz, R.M., 2006. Dividend policy and the earned/contributed
capital mix: a test of the life-cycle theory. Journal of Financial Economics 81, 227-254.
Del Guercio, D., Tkac, P.A., 2002. The determinants of the flow of funds of managed portfolios:
mutual funds versus pension funds. Journal of Financial and Quantitative analysis 37, 523-557.
Dermine, J., Roller, L.H., 1992. Economies of Scale and Scope in French Mutual Funds. Journal
of Financial Intermediation 2, 83-93.
DeYoung, R., 1998. Comments on de novo banks and lending to small businesses. Journal of
Banking and Finance 22, 868-872.
DeYoung, R., Hasan, I., 1998. The performance of de novo banks: a profit efficiency approach.
Journal of Banking and Finance 22, 565-587.
DeYoung, R., Goldberg, L.G., White, L.J., 1999. Youth, adolescence, and maturity of banks:
Credit availability to small business in an era of banking consolidation. Journal of Banking and
Finance 23, 463-492.
Diamond, D.W., 1991. Monitoring and reputation: the choice between bank loans and directly
placed debt. Journal of Political Economy 99, 689-721.
Dickinson, V., 2007. Cash flow patterns as a proxy for firm life cycle. working paper, University
of Florida.
Ding, B., 2006. Mutual fund mergers: a long-term analysis. working paper, State University of
New York at Albany.
Edelen, M.R., Evans, R., Kadlec, B.G., 2007. Scale effects in mutual fund performance: the role
of trading costs. working paper, ReFlow Management, LLC, Boston College, and Virginia Tech.
Fama, E.F., French K.R., 2001. Disappearing dividends: Changing firm characteristics or lower
propensity to pay? Journal of Financial Economics 60, 3-44.
Gaspar, J.M., Masaa, M., Matos, P., 2006. Favoritism in mutual fund families? Evidence on
strategic cross-fund subsidization. Journal of Finance 61, 73-104.
75
Goldberg, L.G., White, L.J., 1998. De novo banks and lending to small business: An empirical
analysis. Journal of Banking and Finance 22, 851-867.
Gruber, M.J., 1996. Another puzzle: the growth in actively managed mutual funds. Journal of
Finance 51, 783-810.
Grullen, G., Michaely, R., Swaminathan, B., 2002. Are dividend changes a sign of firm maturity?
Journal of Business 75 (3), 387-424.
Hong, H., Kubik, J.D., Stein J.C., 2005. The neighbor’s portfolio: word-of-mouth effects in the
holdings and trades of money managers. Journal of Finance 60, 2801-2824.
Hunter, W.C., Srinivasan, A., 1990. Determinants of de novo bank performance. Economics
Review, Federal Reserve Bank of Atlanta 75, 14-25.
Jain, P.C., Wu, J.S., 2000. Truth in mutual fund advertising: Evidence on future performance and
fund flows. Journal of Finance 55, 937-958.
Jayaraman, N., Khorana A., Nelling, E., 2002. An analysis of the determinants and shareholder
wealth effects of mutual fund mergers. Journal of Finance 57, 1521-1551.
Jensen, M., 1986. Agency costs on free cash flow, corporate finance, and takeover. The American
Economic Review 76, 323-329.
Kacperczyk, M., Sialm, C., Zheng, L., 2005. On the industry concentration of actively managed
equity mutual funds. Journal of Finance 60, 1983-2011.
Khorana, A., Servaes, H., 1999. The determinants of mutual fund starts. Review of Financial
studies 12, 1043-1074.
LaPlante, M., 2001. Influences and trends in mutual fund expense ratios. Journal of Financial
Research 24, 45-63.
Lazko, D.A., 1999. Economies of scale in mutual fund administration. Journal of Financial
Research 22, 331-339.
Liu, M., 2008. Accruals and managerial operating decisions over the firm life cycle. working
paper. Pennsylvania State University.
Malhotra, D.K., McLeod, R.W., 1997. An empirical analysis of mutual fund expenses. Journal of
Financial Research 20, 175-190.
Massa, M., 1998. Why so many mutual funds? Mutual fund families, market segmentation and
financial performance. working paper. INSEAD.
Massa, M., 2003. How do family strategies affect fund performance? When performancemaximization is not the only game in tow. Journal of Financial Economics 67, 249-304.
76
Massa, M., Reuter, J., Zitzewitz, E., 2007. When should firms share credit with employees?
Evidence from anonymously managed mutual funds. working paper, INSEAD, University of
Oregon, and Dartmouth College.
McAleer, M., 1995. The significance of testing empirical on-nested models. Journal of
Econometrics 67, 149-171.
Miller, D., Friesen P.H., 1984. A longitudinal study of the corporate life cycle. Management
science 30, 1161-1183.
Nanda, V., Narayanan, M.P., Warther, V.A., 2000. Liquidity, investment ability, and mutual fund
structure. Journal of Financial Economics 57, 417-443.
Nanda V., Wang, Z.J., Zheng, L., 2005. The ABCs of mutual funds: on the introduction of
multiple share classes. working paper. Arizona State University and University of CaliforniaIrvine.
Perold, A.F., Salomon, R.S., 1991. The right amount of assets under management. Financial
Analysts Journal 47, 31-39.
Petersen, M.A., 2007. Estimating standard errors in finance panel datasets: comparing approaches.
Review of Financial Studies, forthcoming.
Pindyck, R.S., 1988. Irreversible investment, capacity choice, and the value of the firm. American
Economic Review 78, 969-985.
Pindyck, R.S., 1991. Irreversibility, uncertainty, and investment. Journal of Economic Literature
29, 1110-1148.
Pollet, J.M., Wilson M., 2007. How does size affect mutual fund behavior? working paper.
niversity of Illinois at Urbana-Champaign and Hong Kong University of Science & Technology.
Quinn, R.E., Cameron, K., 1983. Organizational life cycles and shifting criteria of effectiveness:
some preliminary evidence. Management Science 29, 33-51.
Rea, J.D., Reid, B.K., Millar, K.W., 1999. Operating expense ratios, assets, and economies of
scale in equity mutual funds. Investment Company Institute Perspective 5.
Sirri, E.R., Tufano, P., 1996. Costly search and mutual fund inflows. Journal of Finance 53, 15891622.
Tufano, P., Sevick M., 1997. Board structure and fee-setting in the U.S. mutual fund industry.
Journal of Financial Economics 46, 321-355.
Warner, J.B., Wu, J.S., 2006. Why do mutual fund advisory contracts change? Fund versus
family influence. working paper. University of Rochester.
Wermers, R., 1999. Mutual fund herding and the impact on stock prices. Journal of Finance, 54,
581-622.
77
Wermers, R., 2003. Is money really “smart”? New evidence on the relation between mutual fund
flows, manager behavior, and performance persistence. working paper. University of Maryland.
Zweig, J., 1996. When to take a wild ride. Money (July), 96-99.
Zhao, X., 2004. Why are some mutual funds closed to new investors? Journal of Banking and
Finance 28, 1867-1887.
Zhao, X., 2005. Exit decisions in the U.S. mutual fund industry. Journal of Business 78, 13651401.
78
80
High Growth
Fund Percentage %
70
Low Growth
60
Maturity
Decline
50
40
30
20
10
0
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49
Fund Age
Fig. 1. Percentage of funds located in different life cycle stages by fund age for the period 1961-2005.
This figure shows aspects of a fund’s life cycle path. After using the composite-score measure to classify a
fund’s life cycle stage for all fund-years, for each fund age I calculate the percentage of funds located in the
life cycle stages of high-growth, low-growth, maturity, and decline, respectively. As a result, I obtain four
age-series of percentage of funds.
79
0.0160
0.0140
0.0120
Monthly Returns
0.0100
0.0080
0.0060
0.0040
0.0020
0.0000
-0.0020
High Grow th
Low Grow th
Maturity
Decline
-0.0040
Net Return
S&P500 Excess Return
4-Factor Adjusted Return
Fig. 2. Mutual fund monthly performance over life cycle stages for the period 1961-2005.
This figure shows mutual fund monthly returns over the life cycle stages of high-growth, low-growth,
maturity, and decline, respectively. Net return is the monthly return to investors. S&P500 excess return is
the monthly return adjusted by the return on S&P500 index. 4-factor adjusted return is the monthly return
adjusted by Carhart’s (1997) four factors.
80
0.90
Annual Turnover Ratios
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
High Grow th Low Grow th
Maturity
Decline
Fig.3. Mutual fund annual turnover ratio over life cycle stages for the period 1961-2005.
This figure shows mutual fund annual turnover ratio over the life cycle stages of high-growth, low-growth,
maturity, and decline, respectively. Annual turnover ratio is defined as the minimum of aggregated sales or
aggregated purchases of securities, divided by the average 12-month Total Net Assets of the fund.
81
0.0350
0.0300
0.0250
Fund Flows
0.0200
0.0150
0.0100
0.0050
0.0000
-0.0050
High Grow th Low Grow th
Maturity
Decline
-0.0100
-0.0150
Fig. 4. Mutual fund monthly net flow ratio over life cycle stages for the period 1961-2005.
This figure shows mutual fund monthly net flow ratio over the life cycle stages of high-growth, low-growth,
maturity, and decline, respectively. Flow ratio is calculated as monthly net fund flows divided by Total Net
Assets (TNA) of the fund. It equals [TNAt − TNAt −1 ⋅ (1 + rt )] / TNAt , where rt is the net return of the
month.
82
Table 1
Life cycle stage transition matrices of all sample funds
This table reports stage transition matrices of all sample funds that cover the time period from 1961 to 2005.
P1, P4, and P9, respectively, indicate stage transition matrix in the second, fifth, and tenth year. Each row
shows the transition probabilities to the life cycle stage of high growth, low growth, maturity, and decline.
P1
P4
P9
High Growth
Low Growth
Maturity
Decline
High Growth
0.37
0.07
0.03
0.03
Low Growth
0.41
0.46
0.12
0.09
Maturity
0.16
0.36
0.57
0.20
Decline
0.06
0.11
0.28
0.68
High Growth
Low Growth
Maturity
Decline
High Growth
0.17
0.07
0.04
0.05
Low Growth
0.36
0.29
0.16
0.14
Maturity
0.31
0.41
0.43
0.29
Decline
0.15
0.23
0.36
0.52
High Growth
Low Growth
Maturity
Decline
High Growth
0.07
0.06
0.06
0.06
Low Growth
0.22
0.20
0.18
0.18
Maturity
0.38
0.38
0.37
0.36
Decline
0.32
0.36
0.39
0.41
83
Table 2
Mutual fund prescriptive statistics
This table reports prescriptive statistics for the funds in the sample. N is the number of observation. Net
return is the reported monthly net return. S&P500 excess return is the monthly return adjusted by the return
of S&P500 index. 4-factor adjusted return is the monthly return adjusted by Carhart (1997) four factors.
Expense ratio is the total annual management fees and expenses divided by total net asset. Turnover is the
annual fund turnover. Total net asset is the net asset of the fund after all expenses. Monthly fund flows is
the new fund flow into the fund over a month divided by the TNA. Total load is the total front-end,
deterred and rear-end charges divided by new investments. Industry number is the number of distinct fourdigit SIC code in the portfolio. Stock number is the number of domestic stocks in the portfolio. The sample
covers the time period from January 1961 through December 2005. All variables are winsorized at one and
the 99th percentile.
Variable
Net Return
S&P500 Excess Return
4-Factor Adjusted Return
Expense Ratio
Turnover
Total Net Asset (million)
Monthly Fund Flows
Total Load
Industry Number
Stock Number
N
64946
64946
33547
64495
55069
65000
63220
81692
14493
13680
Mean
Median
Max
Panel A: High Growth Stage
0.0132
0.0048
0.0013
0.0139
1.05
283
0.0653
0.0158
54
86
0.0143
0.0030
0.0002
0.0137
0.73
71
0.0300
0
42
59
0.1696
0.1359
0.0924
0.0311
7.46
4171
1.0363
0.0850
286
611
Min
-0.1540
-0.1038
-0.0737
0
0.02
0.631
-0.1648
0
5
10
Panel B: Low Growth Stage
Net Return
S&P500 Excess Return
4-Factor Adjusted Return
Expense Ratio
Turnover
Total Net Asset (million)
Monthly Fund Flows
Total Load
Industry Number
Stock Number
70891
70891
53639
70698
65670
70926
73096
89700
17899
16153
0.0094
0.0032
-0.0008
0.0127
0.85
755
0.0108
0.0171
57
91
0.0121
0.0023
-0.0008
0.0122
0.65
149
0.0068
0
44
62
0.1397
0.1093
0.0721
0.0270
4.41
13784
0.2241
0.0850
321
737
-0.1446
-0.0926
-0.0688
0
0.03
1.824
-0.1305
0
4
6
84
Panel C: Maturity Stage
Net Return
S&P500 Excess Return
4-Factor Adjusted Return
Expense Ratio
Turnover
Total Net Asset (million)
Monthly Fund Flows
Total Load
Industry Number
Stock Number
73557
73557
57442
73482
68981
73603
73659
98190
21897
18717
0.0071
0.0012
-0.0016
0.0123
0.83
1015
-0.0042
0.0176
53
84
0.0099
0.0010
-0.0016
0.0117
0.64
179
-0.0035
0
43
60
0.1290
0.0969
0.0678
0.0275
3.88
21954
0.1289
0.0850
261
534
-0.1390
-0.0900
-0.0693
0
0.03
1.934
-0.1273
0
3
4
0.1370
0.1018
0.0758
0.0432
5.23
11623
0.1111
0.0850
201
372
-0.1568
-0.1142
-0.0927
0
0.02
0.887
-0.2200
0
2
2
Panel D: Decline Stage
Net Return
S&P500 Excess Return
4-Factor Adjusted Return
Expense Ratio
Turnover
Total Net Asset (million)
Monthly Fund Flows
Total Load
Industry Number
Stock Number
59151
59151
36653
45792
42716
45800
53906
58860
15221
12387
0.0055
-0.0033
-0.0036
0.0139
1.03
692
-0.0186
0.0183
45
70
0.0085
-0.0017
-0.0029
0.0128
0.77
140
-0.0129
0
39
57
85
Table 3
Correlation matrix
This table reports the correlation coefficient between variables. 4-factor adjusted return is the monthly return adjusted by Carhart (1997) four factors. LogTNA is
the natural logarithm of (1+ total net assets). Industry number is the number of distinct four-digit SIC code in the portfolio. Stock number is the number of stocks
in the portfolio. LogFamily is log of (1+ family total assets). Expense ratio is the total annual management fees and expenses divided by total net asset. Turnover
is the annual fund turnover. Flows are the monthly new fund flow divided by TNA. Total load is the total front-end, deterred and rear-end charges divided by
new investments. The sample covers the time period from January 1961 through December 2005.
4-Factor adjusted return
LogTNA
Industry number
Stock number
LogFamily
Expense Ratio
Turnover
Flows
Total load
4-Factor
Adjusted Return
1
0.00
0.01
0.00
0.00
-0.02
-0.01
0.05
-0.02
LogTNA
Industry
Number
Stock
Number
LogFamily
Expense
Ratio
Turnover
Flows
Total load
1
0.27
0.26
0.62
-0.36
-0.11
0.02
0.12
1
0.97
0.28
-0.18
0.00
0.03
-0.01
1
0.26
-0.17
0.02
0.03
-0.02
1
-0.29
0.00
0.02
0.21
1
0.20
0.02
0.35
1
0.02
-0.01
1
0.02
1
86
Table 4
Life cycle effect on performance controlling for scale
This table reports the means and medians of monthly returns of different size quartiles over life cycle
stages. The sample covers the time period from January 1961 through December 2005. Within each life
cycle stage, I rank fund-month observations by size into quartiles, with the fourth quartile having the
largest size. I choose the fourth quartile in the high-growth stage, the third quartile in the low-growth stage,
and the second quartile in both the maturity and decline stages so that the average size of the sample funds
decreases over stages. Net return is the reported monthly return. S&P500 excess return is the net return
adjusted by S&P500 index return. 4-Factor adjusted return is the net return adjusted by Carhart (1997) four
factors.
Stage
High Growth
Low Growth
Maturity
Decline
Quartile
4
3
2
2
TNA
median
959
353
139
99
mean
1389
379
145
104
Net Return
S&P500 Excess Return 4-Factor Adjusted Return
median
mean
median
mean
median
mean
0.0158
0.0134
0.0031
0.0051
0.0000
0.0010
0.0127
0.0091
0.0022
0.0029
-0.0009
-0.0010
0.0099
0.0067
0.0010
0.0011
-0.0019
-0.0019
0.0093
0.0058
-0.0010
-0.0023
-0.0027
-0.0033
87
Table 5
Regression of mutual fund monthly returns on life cycle stages
This table reports results from estimating pooled OLS model with standard errors clustered on fund and
time, random effect model, and fixed effect model. The sample covers the time period from January 1961
through December 2005. The dependent variable is the net return adjusted by Carhart (1997) four factors.
LowGrowth, Maturity, and Decline are dummy variables for life cycle stages. LogTNA is the natural
logarithm of (1+ total net assets). The controlled variables include asset turnover, expense ratios, total load,
fund flows, and fund sector. t-statistics is reported in the parentheses under the coefficients. All
independent variables are lagged for one period. *, **, *** denote a significant difference from zero at the
10%, 5%, and 1% levels, respectively.
Model 1
OLS two-way cluster
-40.64 ***
(-5.17)
Maturity
-51.31 ***
(-5.71)
Decline
-80.37 ***
(-7.67)
LogTNA
-5.404 ***
(-3.45)
LogTNA*LowGrowth
4.568 ***
(3.38)
LogTNA*Maturity
4.843 ***
(3.20)
LogTNA*Decline
7.045 ***
(3.97)
Variable
LowGrowth
Observations
177,361
Model 2
Random Effect
-39.82 ***
(-7.10)
-51.13 ***
(-9.16)
-79.53 ***
(-12.1)
-6.221 ***
(-7.09)
4.368 ***
(4.28)
4.798 ***
(4.77)
7.038 ***
(6.04)
177,361
Model 3
Fixed Effect
-30.18 ***
(-4.57)
-42.04 ***
(-6.11)
-63.92 ***
(-7.85)
-19.35 ***
(-16.97)
2.941 ***
(2.51)
3.627 ***
(3.04)
4.571 ***
(3.27)
177,361
88
Table 6
Regression of mutual fund monthly returns on life cycle stages classified by two alternative measures
This table reports results from estimating pooled OLS regression model with standard errors clustered on
fund and time. The sample covers the time period from January 1961 through December 2005. The
dependent variable is the net return adjusted by Carhart (1997) four factors. LowGrowth, Maturity, and
Decline are dummy variables for life cycle stages. LogTNA is the natural logarithm of (1+ total net assets).
The controlled variables include asset turnover, expense ratios, total load, fund flows, and fund sector. tstatistics is reported in the parentheses under the coefficients. All independent variables are lagged for one
period. *, **, *** denote a significant difference from zero at the 10%, 5%, and 1% levels, respectively.
Variable
LowGrowth
Maturity
Decline
LogTNA
LogTNA*LowGrowth
LogTNA*Maturity
LogTNA*Decline
Observations
Model 1
Score Measure
-40.64
(-5.17)
-51.31
(-5.71)
-80.37
(-7.67)
-5.404
(-3.45)
4.568
(3.38)
4.843
(3.20)
7.045
(3.97)
177,361
***
***
***
***
***
***
***
Model 2
Age Measure
-15.75
(-2.13)
-23.59
(-3.19)
-31.62
(-3.37)
-2.487
(-1.62)
1.320
(0.94)
2.797
(2.05)
3.610
(2.36)
**
***
***
**
**
177,361
89
Table 7
J-test result
The table presents the J-test results of the regression model using the composite-score measure vs. the
regression model using age measure. First, I estimate model 1 and model 2 in Table 6 and calculate the sets
of fitted value for the dependent variable. Then I estimate a regression specification based on model 1,
using the fitted value from model 2 as the added explanatory variable. I also estimate a regression model
based on model 2 using the fitted value from model 1 as the added explanatory variable. t-statistics is
reported in the parentheses under the coefficients. *, **, *** denote a significant difference from zero at the
10%, 5%, and 1% levels, respectively.
Variable
Model 1
Score Measure
Fitted value from Model 1
Fitted value from Model 2
Model 2
Age measure
1.128 ***
(8.17)
-0.420
(-1.62)
90
Table 8
Life cycle stage transition matrices affected by rejuvenation strategies
This table reports the stage transition matrices of sample funds that neither changed investment objective
nor hired more portfolio managers, funds that changed objectives only, and funds that hired more managers
only. The sample covers the time period from 1993 to 2005. P1 indicate the stage transition matrices in the
next year. Each row shows the transition probabilities to the stage of high growth, low growth, maturity,
and decline.
Panel A: Neither changing objective nor hiring more managers
P1
High growth
Low growth
Maturity
Decline
High growth
0.60
0.05
0.02
0.02
Low growth
0.32
0.65
0.07
0.05
Maturity
0.05
0.25
0.71
0.10
Decline
0.03
0.05
0.20
0.83
Low growth
0.32
0.63
0.04
0.08
Maturity
0.02
0.29
0.80
0.23
Decline
0.02
0.03
0.12
0.67
Low growth
0.33
0.65
0.08
0.04
Maturity
0.05
0.25
0.71
0.11
Decline
0.03
0.04
0.19
0.82
Panel B: Changing objective
P1
High growth
Low growth
Maturity
Decline
High growth
0.64
0.05
0.05
0.02
Panel C: Hiring more managers
P1
High growth
Low growth
Maturity
Decline
High growth
0.60
0.05
0.02
0.03
91
Table 9
Multinomial logistic regression of the second year stage transition on rejuvenation strategies
This table reports that result of a multinomial logistic regression of the second year stage transition, to
investigate the effects alternative strategies on stage transition probabilities. The dependent variable has a
categorical value of 0, 1, and 2, which indicate next-year transition to the same, younger, and older life
cycle stages, respectively. LowGrowth, Maturity and Decline are dummies for life cycle stages. Objective
is a dummy variable that equals 1 when the fund changes its investment objective, and 0 otherwise.
Manager is a dummy variable that equals 1 when the fund hires more portfolio managers, and 0 otherwise.
The controlled variables include fund size, expense ratio, turnover, total load, and fund objective. zstatistics is reported in the parentheses under the coefficients. *, **, *** denote a significant difference
from zero at the 10%, 5%, and 1% levels, respectively.
Variable
Objective*HighGrowth
Objective*LowGrowth
Objective*Maturity
Objective*Decline
Manager*HighGrowth
Manager*LowGrowth
Manager*Maturity
Pseudo R2
Observations
Model 1
Rejuvenate vs. Remain
Model 2
Descend vs. Remain
-16.075 ***
(-31.15)
-0.145
(-0.18)
0.260
(0.76)
0.870 ***
(4.23)
-0.052
(-0.12)
-35.396 ***
(-46.35)
-0.229
(-0.58)
-0.206
(-0.59)
-0.077
(-0.28)
-0.133
(-0.23)
-2.656 ***
(-10.45)
-0.375
(-0.63)
0.420
(0.64)
-1.240
(-1.03)
0.12
0.12
9,075
9,075
92
Table 10
Regression of mutual fund three-month returns on life cycle stages
This table reports results from estimating pooled OLS model with standard errors clustered on fund and
time, random effect model, and fixed effect model. The sample covers the time period from January 1961
through December 2005. The dependent variable is the three-month cumulative net return adjusted by
Carhart (1997) four factors. LowGrowth, Maturity, and Decline are dummy variables for life cycle stages.
LogTNA is the natural logarithm of (1+ total net assets). The controlled variables include asset turnover,
expense ratios, total load, fund flows, and fund sector. t-statistics is reported in the parentheses under the
coefficients. All independent variables are lagged for one period. *, **, *** denote a significant difference
from zero at the 10%, 5%, and 1% levels, respectively.
Variable
LowGrowth
Maturity
Decline
LogTNA
LogTNA*LowGrowth
LogTNA*Maturity
LogTNA*Decline
Observations
Model 1
OLS two-way cluster
-122.0 ***
(-5.49)
-145.0 ***
(-6.58)
-225.0 ***
(-8.49)
-17.35 ***
(-4.67)
14.96 ***
(3.88)
14.82 ***
(3.95)
21.18 ***
(4.86)
173,030
Model 2
Random Effect
-103.0
(-9.01)
-121.7
(-10.45)
-190.8
(-14.43)
-33.28
(-17.85)
12.04
(5.92)
11.93
(5.85)
17.71
(7.71)
173,030
***
***
***
***
***
***
***
Model 3
Fixed Effect
-88.900
(-7.40)
-105.899
(-8.52)
-168.411
(-11.98)
-49.665
(-24.4)
10.184
(4.81)
10.057
(4.68)
14.371
(5.95)
***
***
***
***
***
***
***
173,030
93